Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences 13th Edition Haeussler Test Bank

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Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences 13th Edition Haeussler Test Bank

Description

Exam
Name___________________________________

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

1)

The population of a city is given by P = 100,000(1.0 where t is the number of years after 1988. Find the population in
(a) 1988
(b) 1989
(c) 1990.

1)

_____________

2)

The population of a city is given by P = 10,000(1.0 where t is the number of years after 1988. Find the population in
(a) 1988
(b) 1989
(c) 1990.

2)

_____________

3)

For the function f(x) = ,
(a) what is the domain of f?
(b) what is the range of f?

3)

_____________

4)

For the function f(x) = ,
(a) what is the domain of f?
(b) What is the range of f?

4)

_____________

5)

Graph y = f(x) = .

5)

_____________

6)

Graph y = f(x) = .

6)

_____________

7)

Suppose that the number of patients admitted into a hospital emergency room during a certain hour of the day has a Poisson distribution with mean 3. Find the probability that during that hour there will be exactly two emergency patients. Assume that = 0.05.

7)

_____________

8)

If $2000 is invested for 3 years at 8% compounded quarterly, find
(a) the compound amount and
(b) the compound interest.

8)

_____________

9)

If $400 is invested for 2 years at 6% compounded semiannually, find
(a) the compound amount and
(b) the compound interest.

9)

_____________

10)

Suppose $5000 is deposited in a savings account that earns 10% compounded semiannually. What is the value of the account at the end of 6 years? Assume no other deposits or withdrawals.

10)

_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

11)

The population of a city is given by P = 1,000,000(1.0 where t is the number of years after 1987. The population in 1989 was

11)

______

A)

1,040,400.

B)

1,040,000.

C)

1,004,000.

D)

1,020,000.

E)

1,002,000.

12)

Of the following the best approximation of e is

12)

______

A)

1.8.

B)

2.7.

C)

2.3.

D)

3.1.

E)

1.4.

13)

Which of the following is true? If f(x) = , then

13)

______

A)

the domain of f is all positive real numbers and the range is all real numbers.

B)

both the domain and range of f are all real numbers.

C)

the domain of f is all real numbers except zero and the range is all real numbers.

D)

both the domain and range of f are all positive real numbers.

E)

the domain of f is all real numbers and the range is all positive real numbers.

14)

The above graph is best represented by

14)

______

A)

y = ln 4

B)

y =

C)

y =

D)

y =

E)

y =

15)

If $1000 is invested for 2 years at 6% compounded quarterly, then the compound amount at the end of the period is

15)

______

A)

$1141.23.

B)

$1593.84.

C)

$1126.49.

D)

$1123.60.

E)

$1120.00.

16)

If $500 is invested for 3 years at 7% compounded semiannually, then the compound interest at the end of the period is

16)

______

A)

$122.56.

B)

$120.37.

C)

$112.52.

D)

$114.63.

E)

$150.36.

17)

If $10,000 is invested at 16% compounded quarterly, then the compound amount at the end of six years is

17)

______

A)

$26,987.33.

B)

$21,173.75.

C)

$25,633.04.

D)

$26,678.42.

E)

$24,278.09.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

18)

Find the equations of the graph that is obtained from the graph of y = shifted
(a) 3 units down;
(b) 3 units to the right.

18)

_____________

19)

A radioactive element is such that N grams remain after t hours, where How many grams remain after 30 hours?

19)

_____________

20)

A trust fund is being set up by a single payment so that at the end of 30 years there will be $20,000 in the fund. If the interest rate is 8% compounded quarterly, how much money should be paid initially into the trust fund?

20)

_____________

21)

A trust fund is being set up by a single payment so that at the end of 5 years there will be $10,000 in the fund. If the interest rate is 3 % compounded quarterly, how much money should be paid initially into the trust fund?

21)

_____________

22)

By looking at the graph of y = , sketch a graph of y = 3.

22)

_____________

23)

The number of bacteria in a culture is doubling every hour. Currently the culture has 128 bacteria. Make a table of values for the number of bacteria present each hour for 0 to 4 hours. For each hour write an expression for the number of bacteria as a product of 128 and a power of 2. Use the expressions to make an entry in your table for the number of bacteria after t hours. Write a function N for the number of bacteria after t hours.

23)

_____________

24)

The number of bacteria in a culture is growing by 40% every hour. Currently the culture has 500 bacteria. Make a table of values for the number of bacteria present each hour for 0 to 4 hours. For each hour write an expression for the number of bacteria as a product of 500 and a power of 1.4. Use the expressions to make an entry in your table for the number of bacteria after t hours. Write a function N for the number of bacteria after t hours.

24)

_____________

25)

A certain medicine reduces the bacteria present by 25% each day. Currently 28,000 bacteria are present. Make a table of values for the number of bacteria present each day for 0 to 4 days. For each day write an expression for the number of bacteria as a product of 28,000 and a power of 0.75. Use the expressions to make an entry in your table for the number of bacteria after t days. write a function N for the number of bacteria after t days.

25)

_____________

26)

A graphical look at Bacteria Growth: If 100 bacteria are present at the start, the number of bacteria in a culture which changes by constant factor f every hour is given by N(t) = 100( ). Use a graphing calculator to graph this function for various values of f where f > 0. Describe how the graphs where 0 < f < 1 differ from the graphs where f > 1. How does the number of bacteria change when 0 < f < 1? How does the number of bacteria change when f > 1? Describe the graph where How does the number of bacteria change when f = 1?

26)

_____________

27)

Assume an investment is guaranteed to triple every decade.
(a) Make a table of the factor of increase in the investment at each decade for 0 to 3 decades. For each decade, write an expression for the factor of increase as a power of some base.
(b) What base did you use? How does that base relate to the problem?
(c) Use your table to graph the factor of increase as a function of decades.

(d) Use your graph to estimate when the investment will have grown by a factor of 15.

27)

_____________

28)

Assume the amount of paper being recycled quadruples every year.
(a) Make a table of the factor of increase in the amount of paper being recycled at each year for 0 to 3 years. For each year, write an expression for the factor of increase as a power of some base.
(b) What base did you use? How does that base relate to the problem?
(c) Use your table to graph the factor of increase as a function of years.

(d) Use your graph to estimate when the recycling will have grown by a factor
of 50.

28)

_____________

29)

An investment increases by 10% every year. Write a function for the factor of increase in the investment as a function of years. Use a graphing calculator to graph your function. Use the graph to estimate when the investment will double.

29)

_____________

30)

The amount of plastic being recycled increases by 30% every year. Write a function for the factor of increase in plastic recycling as a function of years. Use a graphing calculator to graph your function. Use the graph to estimate when the amount of recycling will triple.

30)

_____________

31)

Assume the value of a sailboat depreciates by every year.
(a) Make a table of the factor of decrease in the value of the sailboat for 0 to 3 years. For each year, write an expression for the factor of decrease in the value of the sailboat as a power of some base.
(b) What base did you use? How does the base relate to the problem?
(c) Use your table to graph the factor of decrease as a function of years.

(d) Use your table to guess when your boat will be worth 25% as much as its
original price.

31)

_____________

32)

Assume the value of a computer depreciates by 30% every year.
(a) Make a table of the factor of decrease in the value of the computer for 0 to 3 years. For each year, write an expression for the factor of decrease in the value of the computer as a power of some base.
(b) What base did you use? How does the base relate to the problem?
(c) Use your table to graph the factor of decrease as a function of years.

(d) Use your graph to guess when your computer will be worth a tenth of its original
price.
(e) Using the table you made, write a function for the depreciation as a function
of years. Use a graphing calculator to graph your function. Use the graph to
estimate when the computer will be worth a tenth of its original value.
Compare this answer with the guess you made from your graph.

32)

_____________

33)

Assume the value of an RV depreciates by 22% every year.
(a) Make a table of the factor of decrease in the value of the RV for 0 to 3 years. For each year, write an expression for the factor of decrease in the value of the RV as a power of some base.
(b) What base did you use? How does the base relate to the problem?
(c) Use your table to graph the factor of decrease as a function of years.

(d) Use your graph to guess when your RV will be worth a tenth of its original
price.
(e) Using the table you made, write a function for the depreciation as a function
of years. Use a graphing calculator to graph your function. Use the graph to
estimate when the RV will be worth a tenth of its original value. Compare this
answer with the guess you made from your graph.

33)

_____________

34)

Assume your $2000 investment,which is guaranteed to triple every decade, has a one time $10 service charge.
(a) Make a table of the value of your investment without the service charge at each decade from 0 to 3.
(b) Make a table of the value of your investment with the service charge deducted at each decade from 0 to 3.
(c) How could you use a graph of (a) to make a graph of (b)?

34)

_____________

35)

Assume your savings consist of a $5000 investment which is guaranteed to increase by 7% every year and $800 cash in a safe at your home.
(a) Make a table of the value of your investment at 0 to 3 years.
(b) Make a table of the value of total savings at 0 to 3 years.
(c) How could you use the graph of (a) to make a graph of (b)? Verify your answer using a graphing calculator.

35)

_____________

36)

Sean and Carley have bacterial infections. Sean was given medicine which reduces the number of bacteria hourly by 20%. 5 hours later Carley began the same treatment.
(a) If y = 0. represents the multiplicative decrease of bacteria for Carley, write an equation using the same reference that represents the multiplicative decrease in the bacteria in Sean.
(b) If a doctor had a graph of the multiplicative decrease of bacteria for Carley, how could she use it to graph the multiplicative decrease of the bacteria in Sean? Verify your answer using a graphics calculator.

36)

_____________

37)

Suppose $2000 is invested at 6.5% compounded annually.
(a) Find the value of the investment after 5 years.
(b) Find the value of the interest which was earned over the first 5 years.

37)

_____________

38)

Suppose $2000 is invested at 6.5% compounded annually.
(a) Find the value of the investment after 10 years.
(b) Find the value of the interest which was earned over the first 10 years.

38)

_____________

39)

Suppose $20,000 is invested at 6.5% compounded annually.
(a) Find the value of the investment after 5 years.
(b) Find the value of the interest which was earned over the first 5 years.

39)

_____________

40)

Suppose $2000 is invested at 6.5% compounded quarterly.
(a) Find the value of the investment after 5 years.
(b) Find the value of the interest which was earned over the first 5 years.

40)

_____________

41)

Suppose $2000 is invested at 6.5% compounded monthly.
(a) Find the value of the investment after 5 years.
(b) Find the value of the interest which was earned over the first 5 years.

41)

_____________

42)

Suppose $2000 is invested at 6.5% compounded daily (exclude extra day for leap year).
(a) Find the value of the investment after 5 years.
(b) Find the value of the interest which was earned over the first 5 years.

42)

_____________

43)

A company is downsizing and expects the number of employees to shrink at the rate of 3% per month. Currently the company employs 30,000 people.
(a) How many people are expected to be employed with this company in 1 year?
(b) Use a graphing calculator to predict the number of months until the number of employees will be half its current size.

43)

_____________

44)

A town of 1400 is growing at the rate of 8% per year. If this rate continues, what will the population of this town be in 20 years?

44)

_____________

45)

The number of yearly visitors to a resort has been shrinking at the rate of 6%. Currently the resort gets 120,000 tourists each year.
(a) If this rate continues, how many tourists will they get in 15 years?
(b) Use a graphing calculator to predict the number of years until the number of tourists will be less than 20,000.

45)

_____________

46)

The multiplicative decrease in purchasing power P after t years of inflation at 3% can be modeled by
Graph the decrease in purchasing power as a function of t years.

46)

_____________

47)

Graph the population for a city with 80,000 people as a function of years if the growth is modeled by

47)

_____________

48)

Graph f(x) =

48)

_____________

49)

Graph g(x) =

49)

_____________

50)

Graph h(x) = 1

50)

_____________

51)

Graph f(x) = 3

51)

_____________

52)

Graph f(x) = 2

52)

_____________

53)

Express = -3 in exponential form.

53)

_____________

54)

Express 64 = 3 in exponential form.

54)

_____________

55)

Express = 81 in logarithmic form.

55)

_____________

56)

Express = in logarithmic form.

56)

_____________

57)

Graph y = f(x) = x.

57)

_____________

58)

For the function f(x) = x,
(a) what is the domain of f?
(b) What is the range of f?

58)

_____________

59)

Evaluate and simplify: log 100

59)

_____________

60)

Evaluate and simplify: ln

60)

_____________

61)

Evaluate and simplify: log (0.1)

61)

_____________

62)

Evaluate and simplify: 1

62)

_____________

63)

Evaluate and simplify: ln

63)

_____________

64)

Evaluate and simplify:

64)

_____________

65)

Evaluate and simplify: (-2)

65)

_____________

66)

Evaluate and simplify: 6

66)

_____________

67)

Find x: x = 3

67)

_____________

68)

Find x: logx = 0

68)

_____________

69)

Find x: ln x = 1

69)

_____________

70)

Find x: x = 2

70)

_____________

71)

Find x: x = -3

71)

_____________

72)

Find x: log x = 3

72)

_____________

73)

Find x: ln x = -2

73)

_____________

74)

Find x: log x = -2

74)

_____________

75)

Find x: 36 = x

75)

_____________

76)

Find x: = x

76)

_____________

77)

Find x: log 100,000 = x

77)

_____________

78)

Find x: 2 = x

78)

_____________

79)

Find x: log 0.01 = x

79)

_____________

80)

Find x: ln = x

80)

_____________

81)

Find x: 16 = 4

81)

_____________

82)

Find x: (x + 4) = 3

82)

_____________

83)

Find x: (4x 1) = 1

83)

_____________

84)

Find x: (4x -3) = 2

84)

_____________

85)

Find x: = x

85)

_____________

86)

Find x and express your answer in terms of natural logarithms: = 2

86)

_____________

87)

Find x and express your answer in terms of natural logarithms: = 6

87)

_____________

88)

A radioactive substance decays according to the equation N = , where N is the number of milligrams present after t days. Find the half-life of the substance.

88)

_____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

89)

The above graph is best represented by

89)

______

A)

x

B)

y =

C)

y =

D)

y = ln 4

E)

y =

90)

Which of the following is true? If f(x) = ln x, then

90)

______

A)

the domain of f is all positive real numbers and the range is all real numbers.

B)

the domain of f is all real numbers and the range is all positive real numbers.

C)

the domain of f is all real numbers except zero and the range is all real numbers.

D)

both the domain and the range of f are all positive real numbers.

E)

both the domain and the range of f are all real numbers.

91)

125 =

91)

______

A)

0

B)

1

C)

2

D)

3

E)

4

92)

log 0.001 =

92)

______

A)

-1

B)

-2

C)

-3

D)

-4

E)

-5

93)

The value of 0 is

93)

______

A)

1

B)

-1

C)

0

D)

3

E)

not defined

94)

=

94)

______

A)

-2

B)

C)

D)

-5

E)

-4

95)

If x = -3, then x =

95)

______

A)

64

B)

C)

-12

D)

E)

81

96)

If (4x + 1) = 3, then x =

96)

______

A)

B)

C)

D)

E)

97)

If (x + 3) = -2, then x =

97)

______

A)

-1

B)

C)

D)

E)

-7

98)

If 5 = 3, then x =

98)

______

A)

B)

C)

D)

E)

ln

99)

If a radioactive substance decays according to the equation N = , where N is the number of milligrams present after t days, then the half-life, in days, of the substance is given by

99)

______

A)

.

B)

.

C)

.

D)

.

E)

.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

100)

Find x: (6 4x ) = 2

100)

____________

101)

A manufacturers supply equation is p = log where q is the number of units supplied at price p per unit. At what price will the manufacturer supply 200 units?

101)

____________

102)

How long will it take for $100 to amount to $200 at an interest rate of 10% compounded annually? Give your answer to 2 decimal places.

102)

____________

103)

Solve for x: 3 =

103)

____________

104)

Solve for x: (2x + 3) = 2

104)

____________

105)

Solve for x: x = 5

105)

____________

106)

Find the domain of y = (x + 1)

106)

____________

107)

True or False: If x = x, then a = b.

107)

____________

108)

Solve the equation for x in terms of y: 1.2y = log

108)

____________

109)

Solve for x: log(98 x + ) = 2

109)

____________

110)

Solve for x: log( + 4x + 104) = 2

110)

____________

111)

Solve for x: y = 3

111)

____________

112)

The work done by 1 kilogram sample of nitrogen as its volume changes from an initial value to a final value of during a constant temperature process is given by W = 3.2 ln . If such a sample expands from a volume of 3 liters to a volume of 5 liters, determine the work done by the gas.

112)

____________

113)

If money is invested at 7% compounded annually and the current amount is 3 times the amount first invested, then the situation can be represented by 3 = . Represent this equation in logarithmic form. What does t represent?

113)

____________

114)

If the yeast has been decreasing by 80% hourly and the current amount is of the amount first measured, then the situation can be represented by = . Represent this equation in logarithmic form. What does t represent?

114)

____________

115)

If a car is depreciating by 12.5% each year and the current amount is 0.5 its original value, then the situation can be represented by 0.5 = . Represent this equation in logarithmic form.

115)

____________

116)

An earthquake measuring 5.8 on the Richter scale can be represented by where I is the intensity of the earthquake and is the intensity of a zero-level earthquake. Represent this equation in exponential form.

116)

____________

117)

If the pH of a substance is 9.2, then the concentration of hydrogen ions h in gram-atoms per liter can be represented by 9.2 = log . Represent this equation in exponential form.

117)

____________

118)

R = log gives the Richter Scale measurement of an earthquake with intensity I where is the intensity of a zero-level earthquake. Make a graph which converts the intensity of the earthquake as compared to a zero-level earthquake to the Richter Scale measurement.

118)

____________

119)

Suppose an investment triples every decade. Graph the number of decades invested as a function of the multiplicative increase in original investment. Label the graph with the name of the function.

119)

____________

120)

Suppose an investment increases by 10% every year. . Graph the number of years invested as a function of the multiplicative increase in original investment. Label the graph with the name of the function.

120)

____________

121)

Suppose a computer decreases in value by 50% every year. Graph the number of years it is owned as a function of the multiplicative decrease in its original value. Label the graph with the name of the function.

121)

____________

122)

Suppose a garbage company has found that garbage per family has decreased by 10% every year since the first year they started a curb-side recycling program. Graph each year as a function of the multiplicative decrease in garbage since the first year of the curb-side recycling program. Label the graph with the name of the function.

122)

____________

123)

The magnitude (Richter Scale) of an earthquake is given by R = log where I is the intensity of the earthquake and is the intensity of a zero-level reference earthquake. represents how many times greater the earthquake is than the reference earthquake. Find the magnitude of an earthquake that is 200 times the intensity of a zero-level earthquake.

123)

____________

124)

The number of years it takes for an amount which is invested at an annual rate of p and compounded continuously to become m times as large is given by t = . How long does it take an investment to quadruple if it is invested at an annual rate of 7% and compounded continuously?

124)

____________

125)

The magnitude (Richter Scale) of an earthquake is given by R = log where I is the intensity of the earthquake and is the intensity of a zero-level reference earthquake. represents how many times greater the earthquake is than the reference earthquake. Find the magnitude of an earthquake that is 2,000,000 times the intensity of a zero-level earthquake.

125)

____________

126)

The number of years it takes for an amount which is invested at an annual rate of p and compounded continuously to become m times as large is given by t = . How long does it take an investment to triple if it is invested at an annual rate of 8% and compounded continuously?

126)

____________

127)

The number of years it takes for an amount which is invested at an annual rate of 7% and compounded continuously to become m times as large is a function of the enlargement factor given t(m) = . Use a graphics calculator to find how many times larger (to the nearest whole number increment) the investment will be in 10, 20, 30, and 40 years.

127)

____________

128)

The magnitude (Richter Scale) of an earthquake is given by R = log where I is the intensity of the earthquake and is the intensity of a zero-level reference earthquake. represents how many times greater than the earthquake is than the reference earthquake. If an earthquake measured 7.5 on the Richter Scale, how many more times intense is it than a barely-felt earthquake?

128)

____________

129)

The magnitude (Richter Scale) of an earthquake is given by R = log where I is the intensity of the earthquake and is the intensity of a zero-level reference earthquake. represents how many times greater than the earthquake is than the reference earthquake. If an earthquake measured 4.2 on the Richter Scale, how many more times intense is it than a zero-level earthquake?

129)

____________

130)

The multiplicative increase m of an investment which is invested at an annual rate of p and compounded continuously for a time t is given by m= . If your annual rate is 6.75%, how many years will it take to double your investment?

130)

____________

131)

Graph f(x) = x

131)

____________

132)

Consider g(x) = (x + 2)
(a) Graph g(x)

(b) Find the domain of g(x)

132)

____________

133)

Consider h(x) = 2ln(x) 3
(a) Graph h(x)

(b) Find the domain of h(x)

133)

____________

134)

Evaluate and simplify:

134)

____________

135)

Evaluate and simplify:

135)

____________

136)

Evaluate and simplify: 1 + 2

136)

____________

137)

Evaluate and simplify: ln + ln 1

137)

____________

138)

Assume that log 6 = 0.7782. Determine the value of log 36.

138)

____________

139)

Assume that log 5 = 0.6690. Determine the value of log 500.

139)

____________

140)

Assume that log 5 = 0.6690. Determine the value of log .

140)

____________

141)

Assume that log 6 = 0.7782. Determine the value of log(0.6).

141)

____________

142)

Assume that log 3 = 0.4771. Determine the value of log 27.

142)

____________

143)

Assume that log 4 = 0.6021. Determine the value of log 400.

143)

____________

144)

Assume that log 4 = 0.6021. Determine the value of log .

144)

____________

145)

Assume that log 3 = 0.4771. Determine the value of log (0.09).

145)

____________

146)

Assume that log 5 = 0.6690 and log 6 = 0.7782. Determine the value of log 30.

146)

____________

147)

Assume that log 5 = 0.6690 and log 6 = 0.7782. Determine the value of log .

147)

____________

148)

Assume that log 3 = 0.4771 and log 4 = 0.6021. Determine the value of log 12.

148)

____________

149)

Assume that log 3 = 0.4771 and log 4 = 0.6021. Determine the value of log 36.

149)

____________

150)

Assume that log 3 = 0.4771 and log 4 = 0.6021. Determine the value of log .

150)

____________

151)

Write the following in terms of ln x and ln(x + 1):

151)

____________

152)

Write the following in terms of ln(x + 2) and ln(x + 4): ln

152)

____________

153)

Write the following in terms of ln(x + 2) and ln(x + 4): ln

153)

____________

154)

Write the following in terms of ln(x + 2) and ln(x + 4): ln

154)

____________

155)

Write the following in terms of ln(x + 2) and ln(x + 4): ln

155)

____________

156)

Write the following in terms of ln(x + 2) and ln(x + 4): ln

156)

____________

157)

Write the following in terms of ln x, ln(x 3), and ln(x + 1):

157)

____________

158)

Write the following in terms of ln x, ln(x 3), and ln(x + 1): ln

158)

____________

159)

Write the following in terms of ln x, ln(x 3), and ln(x + 1):

159)

____________

160)

Express 2 ln 3 ln 4 as a single logarithm.

160)

____________

161)

Express ln 4 (ln 2 + ln 3) as a single logarithm.

161)

____________

162)

Express 2(ln 4 + ln 3 3 ln 2) as a single logarithm.

162)

____________

163)

Express 1 + ln x as a single logarithm.

163)

____________

164)

Express 2 log(x) 3 log(x + 7) as a single logarithm.

164)

____________

165)

Solve for x: ln = x

165)

____________

166)

Solve for x: = 10

166)

____________

167)

Solve for x: = 8

167)

____________

168)

Solve for x: = 20

168)

____________

169)

Solve for x: = 4

169)

____________

170)

If ln 2 = 0.7 and ln 5 = 1.6, find 5.

170)

____________

171)

If log 4 = 0.6 and log 7 = 0.8, find 7.

171)

____________

172)

Write x in terms of natural logarithms.

172)

____________

173)

Write log(x + 3) in terms of natural logarithms.

173)

____________

174)

Write (x + 4) in terms of common logarithms.

174)

____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

175)

=

175)

_____

A)

B)

0

C)

D)

E)

176)

log 10,000 6 log =

176)

_____

A)

-6log

B)

C)

4

D)

0

E)

1

177)

log =

177)

_____

A)

log 3

B)

C)

log 200

D)

3

E)

none of the above

178)

ln e ln 1 =

178)

_____

A)

0

B)

1

C)

6

D)

E)

n(e 1)

179)

ln 6 + ln + ln =

179)

_____

A)

0

B)

1

C)

2

D)

3

E)

4

180)

If log 3 = 0.4771, then log 0.3 =

180)

_____

A)

-0.5229.

B)

-4.771.

C)

-1.4771.

D)

1.4441.

E)

0.5229.

181)

If log 2 = 0.3010 and log 3 = 0.4771, then log 18 =

181)

_____

A)

1.2552.

B)

2.3343.

C)

0.0685.

D)

0.1761.

E)

1.9030.

182)

If log 2 = 0.3010 and log 3 = 0.4771, then log =

182)

_____

A)

0.2136.

B)

2.8239.

C)

1.3801.

D)

0.4259.

E)

1.8927.

183)

If log 2 = 0.3010 and log 3 = 0.4771, then log =

183)

_____

A)

3.1761.

B)

04.283.

C)

1.7323.

D)

1.1303.

E)

0.1761.

184)

If log(x + = 4, then x can equal

184)

_____

A)

.

B)

-3.

C)

.

D)

7.

E)

12.

185)

If ln = 6, then x =

185)

_____

A)

ln .

B)

1.

C)

.

D)

2.

E)

.

186)

If = 5, then x =

186)

_____

A)

.

B)

1.

C)

0.

D)

log 5.

E)

5.

187)

If = 7, then x =

187)

_____

A)

-2.

B)

ln .

C)

2.

D)

1.

E)

0.

188)

ln =

188)

_____

A)

ln x + (ln y ln z)

B)

C)

ln x

D)

ln x (ln y + ln z)

E)

ln x (ln y ln z)

189)

=

189)

_____

A)

ln 2 ln x ln y ln 3 ln z

B)

2 ln x ln y 3 ln z

C)

2(ln x + ln y) 3 ln z

D)

ln 2 + ln x + ln y ln 3 ln z

E)

190)

Writing 2 ln x ln y + 4 ln z as a single logarithm gives

190)

_____

A)

ln( + ).

B)

ln .

C)

.

D)

ln .

E)

ln .

191)

Writing [ln x 2(ln y + 2 ln z)] as a single logarithm gives

191)

_____

A)

ln .

B)

ln .

C)

.

D)

ln .

E)

.

192)

If log 2 = 0.3010 and log 3 = 0.4771, then 3 =

192)

_____

A)

0.4471 0.3010

B)

C)

D)

(0.3010)(0.4771)

E)

0.3010 0.4771

193)

Changing (4x) to natural logarithms gives

193)

_____

A)

.

B)

.

C)

.

D)

ln (4x).

E)

.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

194)

Assume x = 2; y = .12. Find 3x .

194)

____________

195)

Assume ln x = 2; ln y = 7. Find ln( ).

195)

____________

196)

Given ln x = 7.1; ln y = 8.2, find ln( )

196)

____________

197)

Given ln x = 7.1; ln y = 8.2, find ln .

197)

____________

198)

Solve for x: = 8

198)

____________

199)

Simplify:

199)

____________

200)

Simplify:

200)

____________

201)

The population of India was 651 million in 1980 and has been growing at a rate of 2% per year. The population t years later is approximated by N(t) = . Estimate the population in India in the year 2010.

201)

____________

202)

The population in the state of California is 24 million today. It is increasing at a rate of 0.9% per year. The population t years from now is given by the rule P = 24 . After how many years will the population double?

202)

____________

203)

Use a graphing calculator to approximate the solution = 20.

203)

____________

204)

How much more on the Richter Scale is an earthquake with intensity 300,000 times the intensity of a zero-level earthquake than an earthquake with intensity 150,000 times the intensity of a zero-level earthquake? Write as an expression involving logarithms. Simplify by combining logarithms and then use a calculator to evaluate.

204)

____________

205)

What is the sum of the Richter Scale measurement of an earthquake which is 37,000 times the intensity of a zero-level earthquake and an earthquake with intensity 1000 times the intensity of a zero-level earthquake? Write as an expression involving logarithms. Simplify by combining logarithms and then use a calculator to evaluate.

205)

____________

206)

What is the sum of the Richter Scale measurement of an earthquake which is 250,000 times the intensity of a zero-level earthquake and an earthquake with intensity twice the intensity of a zero-level earthquake? Write as an expression involving logarithms. Simplify by combining logarithms and then use a calculator to evaluate.

206)

____________

207)

If an earthquake is times as intense as a zero-level earthquake, what is its measurement on the Richter Scale? Write as logarithmic expression and simplify.

207)

____________

208)

If an earthquake is times as intense as a zero-level earthquake, what is its measurement on the Richter Scale? Write as logarithmic expression and simplify.

208)

____________

209)

If an earthquake is times as intense as a zero-level earthquake, what is its measurement on the Richter Scale? Write as a logarithm expression and simplify.

209)

____________

210)

What power of 3 is 36?

210)

____________

211)

What power of 6 is 36?

211)

____________

212)

What power of 18 is 36?

212)

____________

213)

What power of 9 is 36?

213)

____________

214)

What power of is 36?

214)

____________

215)

Steve wants to use his graphing calculator to check his sketch of y = x but his calculator does not make calculations. Find two equations he could use.

215)

____________

216)

April wants to use her graphing calculator to check her sketch of y = x but her calculator does not make calculations. Find two equations she could use.

216)

____________

217)

Brett wants to use his graphing calculator to check his sketch of y = x but his calculator does not make calculations. Find two equations he could use. Use a graphing calculator to confirm that the two equations are equivalent.

217)

____________

218)

Hannah wants to use her graphing calculator to check this sketch of y = x but her calculator does not make calculations. Find two equations she could use. Use a graphing calculator to confirm that the two equations are equivalent.

218)

____________

219)

Use the change base formula and your graphing calculator to graph
f(x) = x

219)

____________

220)

Use the change base formula and your graphing calculator to graph
f(x) = -3 (x + 4) + 1

220)

____________

221)

Find x and express your answer in terms of common logarithms: = 3

221)

____________

222)

Find x and express your answer in terms of common logarithms: = 4

222)

____________

223)

Find x and express your answer in terms of natural logarithms: 3 = 8

223)

____________

224)

Solve for x: ln(x + 3) = ln(2x)

224)

____________

225)

Solve for x: log x = log 3 + 2 log 4

225)

____________

226)

Solve for x: = 2

226)

____________

227)

Solve for x: ln x + ln 3 = ln(x + 1)

227)

____________

228)

Solve for x: ln(x + 1) ln x = ln 2

228)

____________

229)

Solve for x: log(x + 1) log(x 2) = 1

229)

____________

230)

Solve for x: =

230)

____________

231)

Solve for x: (x 4) + 3 = x

231)

____________

232)

If p = , by using common logarithms express q in terms of p.

232)

____________

233)

Solve for t: 300 = 500(1 ). Assume that ln(0.4) = -0.9.

233)

____________

234)

The demand equation for a product is given by q = 1000 . Solve for p and express your answer in terms of common logarithms.

234)

____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

235)

If ln x + ln 2 = ln 5, then x =

235)

_____

A)

.

B)

.

C)

3.

D)

.

E)

.

236)

If = , then x =

236)

_____

A)

-7.

B)

10.

C)

3.

D)

-4.

E)

6.

237)

If p = , then in terms of common logarithms, q =

237)

_____

A)

5 .

B)

p 4 log 5.

C)

5 .

D)

4 .

E)

.

238)

Initially, three are 50 milligrams of a radioactive substance. The substance decays according to the equation N = 50 , where N is the number of milligrams present after t hours. The number of hours it takes for 10 milligrams to remain is

238)

_____

A)

50 .

B)

.

C)

.

D)

.

E)

.

239)

If (x + 6) = 2 x, then x =

239)

_____

A)

10.

B)

4.

C)

8.

D)

-4.

E)

2.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

240)

Solve for x: (x + 7) 3 2 = x

240)

____________

241)

Solve for x: ( = 129.3

241)

____________

242)

Solve for x: = 7

242)

____________

243)

Solve for x: 2 3 = 0

243)

____________

244)

Find x if 7 = 1

244)

____________

245)

Solve: = 27

245)

____________

246)

Your friend started a savings plan with 2 pennies and each day he doubled the amount saved. Later you started a savings plan with 4 pennies and each day you quadrupled the amount saved. Your friend has been saving for 6 less than 3 times as many days as you. In two days you will put the same amount in savings as your friend. How many days have you been saving?

246)

____________

247)

April took a number and multiplied it by a power of 9. Bob started with the same number and got the same result when he multiplied it by 27 raised to a number which was four less than the exponent that April used. What power of 9 did April use?

247)

____________

248)

Your friend started a savings plan with 3 pennies and each day she saved three times the amount she saved the previous day. Later you started a savings plan with 9 pennies and each day you saved 9 times the amount you saved the previous day. On the day that your friend had been saving for 8 less than 4 times as many days as you, you saved the same amount as your friend. How many days have you been saving?

248)

____________

249)

The value of an investment of $1000 earning 8% compounded yearly is given by A = 1000(1.0 , where t is the number of years it has been invested .If the amount of your investment is now $4000, how long has it been invested?

249)

____________

250)

The sales manager of a department store finds that its daily sales begins to fall after the end of a promotional campaign. The sales in dollars as a function of the number of days after the campaigns end is given by S(d) = 36,000 . If she does not want sales to drop below 30,000 per day before starting a new campaign, when should she start a new campaign?

250)

____________

251)

The value of an investment of $3000 earning 7.25% compounded yearly is given by A = 3000(1.072 , where t is the number of years it has been invested. If the amount of your investment is now $10,000, how long has it been invested?

251)

____________

252)

The demand function for a product is p = 45 where q is the number of units and p is the price of one unit. At what price will the demand be 5 units? How many units will be demanded if the price is $12.42?

252)

____________

253)

The demand function for a product is p = 90 where q is the number of units and p is the price of one unit. At what price will the demand be 5 units? How many units will be demanded if the price is $18.00?

253)

____________

254)

The demand function for a product is p = 180 where q is the number of units and p is the price of one unit. At what price will the demand be 15 units? How many units will be demanded if the price is $24.91?

254)

____________

255)

The demand function for a product is p = 60 where q is the number of units and p is the price of one unit. At what price will the demand be 15 units? How many units will be demanded if the price is $41.60?

255)

____________

256)

An earthquake which is 48,000 times as intense as a zero-level earthquake has a magnitude on the Richter Scale which is 1.7 less than the intensity of another earthquake. What is the intensity of the other earthquake?

256)

____________

257)

An earthquake which is 520,000 times as intense as a zero-level earthquake has a magnitude on the Richter Scale which is 2.7 more than the intensity of another earthquake. What is the intensity of the other earthquake?

257)

____________

258)

An earthquake which is 7200 times as intense as a zero-level earthquake has a magnitude on the Richter Scale which is 3.6 less than the intensity of another earthquake. What is the intensity of the other earthquake?

258)

____________

1)

(a) 100,000
(b) 103,000
(c) 106,090

2)

(a) 10,000
(b) 10,400
(c) 10, 816

3)

(a) all real numbers
(b) all positive real numbers

4)

(a) all real numbers
(b) all positive real numbers

5)

6)

7)

0.225

8)

(a) $2536.48
(b) $536.48.

9)

(a) $450.20
(b) $50.20

10)

$8979.28

11)

A

12)

B

13)

E

14)

B

15)

C

16)

D

17)

C

18)

(a) y = 3
(b) y =

19)

8.634 gms

20)

$1857.85

21)

$8297.54

22)

Shift the graph 2 units to the left and 3 units down.

23)

Equation N(t) = 128

24)

Equation N(t) = 500

25)

Equation N(t) = 28,000(0.7

26)

The graphs for 0 < f < 1 rapidly decrease to the x-axis. The graphs for f > 1 rapidly increase from the x-axis. When 0 < f < 1, the number of bacteria is decreasing. When f > 1, the number of bacteria is increasing. The graph for f = 1 is a horizontal line. The number of bacteria does not change when f = 1.

27)

(a)

(b) 3; The investment triples every decade.
(c)

(d) about 2.5 decades or 25 years

28)

(a)

(b) 4; The recycling quadruples every year.
(c)

(d) about 2.8 years

29)

f(t) = 1. ; about 7.3 years

30)

f(t) = 1. ; about 4.2 years

31)

(a)

(b) ; The boat depreciates by every year .
(c)

(d) Answers will vary.

32)

(a)

(b) 0.7; The computer depreciates by 30% every year (1 1(0.3) = 1 0.3 = 0.7).
(c)

(d) Answers will vary.
(e) f(t) = 0. ; about 6.5 years

33)

(a)

(b) 0.78; The RV depreciates by 22% every year (1 1(0.22) = 1 0.22 = 0.78).
(c)

(d) Answers will vary.
(e) f(t) = 0. ; about 9.3 years

34)

(a), (b)

(c) Shift the graph down 10 units.

35)

(a), (b)

(c) Shift the graph up 800 units.

36)

(a) y = 0.
(b) Shift the graph 5 units to the left.

37)

(a) $2740.17
(b) $740.17

38)

(a) $3754.27
(b) $1754.27

39)

(a) $27,401.73
(b) $7,401.73

40)

(a) $2760.84
(b) $760.84

41)

(a) $2765.63
(b) $765.63

42)

(a) $2767.98
(b) $767.98

43)

(a) 20,815 people
(b) about 23 months

44)

6525 people

45)

(a) 47,435 tourists
(b) about 29 years

46)

47)

48)

Graph of f(x) =

49)

Graph of g(x) =

50)

Graph of h(x) = 1

51)

Graph of f(x) = 3

52)

Graph of f(x) = 2

53)

=

54)

= 64

55)

81 = 4

56)

log = -3

57)

58)

(a) all positive real numbers
(b) all real numbers

59)

2

60)

3

61)

-1

62)

0

63)

64)

-4

65)

not defined

66)

1

67)

27

68)

1

69)

e

70)

16

71)

72)

1000

73)

74)

75)

2

76)

-2

77)

5

78)

79)

-2

80)

3

81)

2

82)

4

83)

84)

1, 3

85)

6

86)

87)

88)

17.33 days

89)

A

90)

A

91)

D

92)

C

93)

E

94)

A

95)

D

96)

A

97)

C

98)

A

99)

A

100)

1

101)

$2.09

102)

7.27 years

103)

x = 9

104)

x = 3

105)

x =

106)

all real numbers greater than -1

107)

False. Example: x = 1, a = 7, b = 3.

108)

1.2

109)

x = -1, 2

110)

x = -2

111)

x =

112)

163.4642

113)

t = 3; the number of times the investment has been compounded.

114)

t = ; the number of hours the yeast has been decreasing

115)

t = 0.5; the number of years the car has been depreciating

116)

=

117)

=

118)

119)

120)

121)

122)

123)

approximately 2.3

124)

approximately 19.8 years.

125)

approximately 6.3

126)

approximately 13.7 years.

127)

approximately 2 times as large; approximately 4 times as large; approximately 8 times as large; approximately 16 times as large

128)

= 31,622,776.6 times as intense

129)

= 15,848.9 times as intense

130)

approximately 10.3 years

131)

Graph of f(x) = x

132)

a) Graph of g(x) = (x + 2)

b) The domain of g(x) is all real numbers greater than -2.

133)

a)

b) The domain of h(x) is all positive real numbers.

134)

4

135)

136)

1

137)

2

138)

1.5564

139)

2.6690

140)

0.2230

141)

-0.2218

142)

1.3413

143)

2.6021

144)

-1.2042

145)

-1.0458

146)

1.4472

147)

0.1092

148)

1.0792

149)

1.5563

150)

0.1250

151)

4 ln x 3 ln (x + 1)

152)

2 ln(x + 2) + ln(x + 4)

153)

ln(x + 2) + ln(x + 4)

154)

155)

ln(x + 2) ln(x + 4)

156)

-2 ln(x + 2) 3 ln(x + 4)

157)

ln(x + 1) 2 ln x ln(x 3)

158)

ln x +

159)

ln x + 2 ln(x 3) ln(x + 1)

160)

ln

161)

ln = ln

162)

ln

163)

ln(ex)

164)

165)

0

166)

2

167)

2

168)

5

169)

1

170)

171)

172)

173)

174)

175)

D

176)

E

177)

A

178)

B

179)

C

180)

A

181)

A

182)

D

183)

D

184)

D

185)

D

186)

E

187)

D

188)

D

189)

C

190)

B

191)

D

192)

C

193)

E

194)

3.24

195)

16

196)

78.7

197)

-36.1

198)

x = 2

199)

200)

201)

1186.2 million

202)

77 years

203)

no solution

204)

log(300,000) log(150,000) = log
= log(2) 0.3

205)

log(37,000) + log(1,000) = log(37,000 1,000)
= log(37,000,000)
7.568

206)

log(250,000) + log(2) = log(250,000 2)
= log(500,000)
5.7

207)

log( ) = x + 2

208)

log = 3(x -1)

209)

log( ) = log( ) = x

210)

3.26

211)

= 2

212)

1.24

213)

1.63

214)

= 0.5

215)

y = ; y =

216)

y = ; y =

217)

y = ; y =

218)

y = ; y =

219)

The graph of f(x) = x

220)

Thegraph of f(x) = -3 (x + 4) + 1

221)

222)

223)

224)

3

225)

48

226)

227)

228)

1

229)

230)

231)

6

232)

q =

233)

234)

235)

D

236)

B

237)

D

238)

D

239)

E

240)

1

241)

x = .6443547

242)

x = = 1.4

243)

x = = 1.5849625

244)

-.6486367

245)

3

246)

8 days

247)

12

248)

4 days

249)

a little over 18 years

250)

Day 15

251)

a little over 17.2 years

252)

$20.12; 8 units

253)

$40.25; 10 units

254)

$60.00; 27 units

255)

$20.00; 5 units

256)

The other earthquake is 2,405,698.7 times as intense as a zero-level earthquake.

257)

The other earthquake is 1037.5 times as intense as a zero-level earthquake.

258)

The other earthquake is 28,663,716.3 times as intense as a zero-level earthquake.

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