College Algebra 8th Edition by Ziegler Byleen Barnett Test Bank

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College Algebra 8th Edition by Ziegler Byleen Barnett Test Bank

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Chapter 5

1. Evaluate to four significant digits.
Ans: 22.27
Section: 5.1

2. Evaluate e9 e9 to four significant digits.
A) 8103 B) 8107 C) 8111 D) 8115
Ans: A Section: 5.1

3. Simplify.
(47x)10y
Ans: 470xy
Section: 5.1

4. Graph y = 4ex.
Ans:
Section: 5.1

5. Graph y = 5ex.
A) C)
B) D)
Ans: B Section: 5.1

6. Find the equations of any horizontal asymptotes without graphing.
y = + 8
A) y = 0 B) y = 8 C) y = 8 D) No horizontal asymptote
Ans: D Section: 5.1

7. Find the equations of any horizontal asymptotes without graphing.
y = ex 7
Ans: y = 7
Section: 5.1

8. Graph y = ex 3.
Ans:
Section: 5.1

9. Graph y = ex 2.
A) C)
B) D)
Ans: D Section: 5.1

10. Solve.
56x = 52x + 8
Ans: 2
Section: 5.1

11. Solve.

A) 3 B) 4 C) 5 D) 4
Ans: C Section: 5.1

12. Solve.
= 1000
Ans:
Section: 5.1

13. Solve.
x2ex + 4xex = 0
A) 0 B) 4 C) 0, 4 D) 0, 4
Ans: D Section: 5.1

14. Solve the exponential equation.
100x 3 = 1000x
Ans: 6
Section: 5.1

15. Graph .
Ans:
Section: 5.1

16. Graph .
Ans:
Section: 5.1

17. Graph f(x) = ex + 2 3.
Ans:
Section: 5.1

18. Simplify.

A) B) C) D)
Ans: D Section: 5.1

19. Simplify.

A) 0 B) C) D)
Ans: C Section: 5.1

20. If you invest $4,500 in an account paying 2% compounded continuously, how much money will be in the account at the end of 4 years?
A) $4,874.79 B) $4,879.93 C) $4,884.77 D) $4,888.11
Ans: A Section: 5.1

21. If you invest $4,500 in an account paying 9.86% compounded continuously, how much money will be in the account at the end of 8 years? Round your answer to the nearest cent.
Ans: $9,903.39
Section: 5.1

22. If $5,000 is deposited into an account earning 8% compounded weekly, and, at the same time, $7,000 is deposited into an account earning 6% compounded weekly, will the first account ever be worth more than the second? If so, when?
Ans: Yes, after 877 weeks
Section: 5.1

Use the following to answer questions 23-24:

The bacteria in a certain culture double every 7.9 hours. The culture has 2,000 bacteria at the start.

23. Write an equation that gives the number of bacteria A in the culture after t hours.
Ans: A = 3,000(2t/7.8)
Section: 5.2

24. How many bacteria will the culture contain after 4 hours?
A) 3,306 bacteria B) 3,409 bacteria C) 3,508 bacteria D) 3,628 bacteria
Ans: B Section: 5.2

Use the following to answer questions 25-26:

A certain geographic region has a population of about 42,000,000 and a doubling time of 32 years. Assume that the growth continues at the same rate.

25. Find the population in 5 years to two significant digits.
Ans: 57,000,000 people
Section: 5.2

26. Find the population in 16 years to two significant digits.
A) 30,000,000 people C) 32,000,000 people
B) 31,000,000 people D) 33,000,000 people
Ans: D Section: 5.2

Use the following to answer questions 27-28:

The radioactive element americium-241 has a half-life of 432 years. Suppose we start with a 20-g mass of americium-241.

27. How much will be left after 377 years? Compute the answer to three significant digits.
A) 10.9 g B) 12.0 g C) 13.2 g D) 13.8 g
Ans: A Section: 5.2

28. How much will be left after 486 years? Compute the answer to three significant digits.
Ans: 9.17 g
Section: 5.2

29. The population of a certain geographic region is approximately 111 million and grows continuously at a relative growth rate of 1.17%. What will the population be in 8 years? Compute the answer to three significant digits.
A) 121 million people C) 123 million people
B) 122 million people D) 124 million people
Ans: B Section: 5.2

30. The nuclear energy source on a certain space vehicle has a power output of P watts after t days as given by
P = 70e0.0025t.
Graph this function for 0 t 100.
Ans:
Section: 5.2

31. In a certain marine zone, the intensity I of light d feet below the surface is given approximately by
I = I0e0.028d
where I0 is the intensity of light at the surface. To the nearest percent, what percentage of the surface light will reach a depth of 15 feet?
Ans: 66%
Section: 5.2

Use the following to answer questions 32-34:

An employee is hired to assemble toys. The learning curve

gives the number of toys the average employee is able to assemble per day after t days on the job.

32. How many toys can the average employee assemble per day after 6 days of training? Round to the nearest integer.
A) 24 toys B) 25 toys C) 26 toys D) 27 toys
Ans: B Section: 5.2

33. How many toys can the average employee assemble per day after 13 days of training? Round to the nearest integer.
Ans: 44 toys
Section: 5.2

34. Does N approach a limiting value as t increases without bound? Explain.
Ans: Yes, N approaches 60 as t increases without bound. This is the upper limit for the number of toys an employee can assemble per day.
Section: 5.2

Use the following to answer questions 35-36:

Radioactive Studies
Time in Hours
x Grams of Material
y
0.1 2
1 1.2
2 0.6
3 0.3
4 0.2
5 0.1
6 0.06

35. Find an exponential regression model of the form y = abx for the data set.
Ans: y = 2.0629(0.5495)x
Section: 5.2

36. Estimate the amount of material remaining after 7 hours. Round to four decimal places.
Ans: 0.0312 grams
Section: 5.2

Use the following to answer questions 37-39:

x y
0 8
10 20
20 54
30 104
40 191
50 359
60 412
70 429

37. Find a logistic regression model for the data.
A) C)
B) D)
Ans: D Section: 5.2

38. Use the model to find the approximate value of y when x = 55.
A) 340 B) 360 C) 380 D) 400
Ans: C Section: 5.2

39. Using the model, what is the projected value of y when x = 70? Why does this differ from the value in the table?
Ans: 439; The model only approximates the data.
Section: 5.2

40. Write in exponential form.
log 6 36 = 2
Ans: 36 = 62
Section: 5.3

41. Write in exponential form.
log 10 0.0001 = 4
A) 0.0001 = 104 C) 10 = (0.0001)4
B) 0.0001 = (4)10 D) 10 = (4)0.0001
Ans: A Section: 5.3

42. Write in exponential form:

Ans: = 52
Section: 5.3

43. Write in exponential form.

Ans: = 161/2
Section: 5.3

44. Write in logarithmic form.
243 = 35
A) log 3 5 = 243 B) log 5 3 = 243 C) log 3 243 = 5 D) log 243 3 = 5
Ans: C Section: 5.3

45. Write in logarithmic form.
64 = 43
Ans: log 4 64 = 3
Section: 5.3

46. Write in logarithmic form.
= 253/2
Ans:
Section: 5.3

47. Write in logarithmic form.
= 42
Ans:
Section: 5.3

48. Simplify.
log 4 1
A) 0 B) 1 C) 4 D) 16
Ans: A Section: 5.3

49. Simplify.
log 16 16
Ans: 1
Section: 5.3

50. Simplify.
log 3 3
A) 0 B) 1 C) 3 D) 9
Ans: B Section: 5.3

51. Simplify.
log 2 27
A) 0 B) 1 C) 2 D) 7
Ans: D Section: 5.3

52. Simplify.
log 4 16
Ans: 2
Section: 5.3

53. Simplify.
log 3 9
A) B) C) 2 D) 2
Ans: C Section: 5.3

54. Simplify.
log 2
A) B) C) 5 D) 5
Ans: D Section: 5.3

55. Simplify.

A) 0 B) 1 C) 4 D) 7
Ans: D Section: 5.3

56. Use a calculator to find log 20,630. Round your answer to four decimal places.
Ans: 4.3145
Section: 5.3

57. Use a calculator to find Round your answer to four decimal places.
A) 3.6144 B) 3.6357 C) 3.7479 D) 3.7661
Ans: A Section: 5.3

58. Use a calculator to find . Round your answer to four decimal places.
Ans: 5.3471
Section: 5.3

59. Use a calculator to find log 5 57. Round your answer to four decimal places.
A) 2.3611 B) 2.5001 C) 2.5121 D) 2.8251
Ans: C Section: 5.3

60. Use a calculator to find log 4 148.79. Round your answer to four decimal places.
Ans: 3.6086
Section: 5.3

61. Evaluate x to four significant digits.
log x = 0.139
Ans: 1.377
Section: 5.3

62. Evaluate x to four significant digits.
ln x = 1.445
A) 0.2357 B) 0.2711 C) 0.3589 D) 0.4513
Ans: A Section: 5.3

63. Solve.
log 3 x = 2
Ans: 9
Section: 5.3

64. Solve.
log b 81 = 2
Ans: 9
Section: 5.3

65. Solve.
log 16 32 = x
A) B) C) 2 D)
Ans: B Section: 5.3

66. Evaluate to three decimal places.

Ans: 0.858
Section: 5.3

67. Use the properties of logarithms to write the expression in terms of and

Ans: log x + 7log y
Section: 5.3

68. Use the properties of logarithms to write the expression as a single log.
log b x + 6 log b y
Ans:
Section: 5.3

69. Use the properties of logarithms to write the expression as a single log.
7ln(x + 1) + 6ln(x)
Ans:
Section: 5.3

70. Given that and find
A) B) 1 C) D)
Ans: B Section: 5.3

71. Given that and find .
A) 180 B) 4,500 C) 27 D) 161
Ans: C Section: 5.3

72. Graph the logarithmic function.
f(x) = log 3 x + 2
Ans:
Section: 5.3

73. Graph the logarithmic function.
f(x) = log 3 (x 1)
A)

B)

C)

D)

Ans: B Section: 5.3

74. Graph the logarithmic function.
f(x) = log 3(x + 2)
Ans:
Section: 5.3

75. Graph the logarithmic function.
f(x) = ln(x + 1)
Ans:
Section: 5.3

76. Find f 1 if f(x) = log 8 x.
Ans: f 1(x) = 8x
Section: 5.3

77. Find f 1 if f(x) = 2log 8 (x 3).
A) f 1(x) = 82x 3 C) f 1(x) = 8x/2 3
B) f 1(x) = 82x + 3 D) f 1(x) = 8x/2 + 3
Ans: D Section: 5.3

78. Find f 1 if f(x) = 6 3 log(x + 2).
Ans: f 1(x) = 100(10-x/3) 2
Section: 5.3

The decibel level D of a sound is defined as

where I is the intensity of the sound measured in watts per square meter, and I0 is the intensity of the least audible sound, standardized to be I0 = 1012 watts per square meter.

79. A rock concert has a volume with an intensity of I = 1.0 101 W/m2. Find its rating in decibels.
Ans: 110 dB
Section: 5.4

80. A radio is playing at a volume with an intensity of I = 5.6 106 W/m2. Find its rating in decibels to two significant digits.
A) 77 dB B) 67 dB C) 60 dB D) 56 dB
Ans: B Section: 5.4

The magnitude on the Richter scale of an earthquake is given by the equation

where E is the energy released by the earthquake, measured in joules, and E0 is the energy released by a very small reference earthquake, standardized at E0 = 104.40 joules.

81. An earthquake has an energy release of 4.93 108 joules. What was its magnitude on the Richter scale?
A) 2.6 B) 2.7 C) 2.8 D) 2.9
Ans: D Section: 5.4

82. If one earthquake measures 5.2 on the Richter scale, and another measures 6.2, how many times more powerful was the 6.2 earthquake? Round to the nearest whole number.
Ans: 32 times as powerful
Section: 5.4

The velocity v of a rocket at burnout (depletion of fuel supply) is given by

where c is the exhaust velocity of the rocket engine, Wt is the takeoff weight (fuel, structure, and payload), and Wb is the burnout weight (structure and payload).

83. A rocket has a weight ratio Wt/Wb = 18.2 and an exhaust velocity c = 2.34 kilometers per second. What is its velocity at burnout? Compute the answer to two decimal places.
A) 6.06 km/s B) 6.44 km/s C) 6.79 km/s D) 7.20 km/s
Ans: C Section: 5.4

84. A rocket has a weight ratio Wt/Wb = 7.6 and an exhaust velocity c = 6.8 kilometers per second. What is its velocity at burnout? Compute the answer to two decimal places.
Ans: 13.79 km/s
Section: 5.4

The pH scale is defined as
pH = log[H+]
where [H+] is the hydrogen ion concentration, in moles per liter. Substances with a pH less than 7 are acidic, and those with a pH greater than 7 are basic.

Use the following to answer questions 85-86:

A solution has a hydrogen ion concentration of [H+] = 9.5 108.

85. Find the pH of the solution. Round your answer to one decimal place.
A) 8.3 B) 8.4 C) 8.5 D) 8.6
Ans: B Section: 5.4

86. Is the solution acidic or basic?
A) Acidic B) Basic
Ans: B Section: 5.4

Use the following to answer questions 87-88:

A solution has a hydrogen ion concentration of [H+] = 9.5 103.

87. Find the pH of the solution. Round your answer to one decimal place.
Ans: 4.1
Section: 5.4

88. Is the solution acidic or basic?
A) Acidic B) Basic
Ans: A Section: 5.4

Use the following to answer questions 89-91:

The following table shows the number of pounds a person lost since beginning a diet.
Time
(days) Pounds Lost
7 2
14 12
21 17
28 20
35 22.5
42 24
49 25
56 25.5

89. Find a logarithmic regression model for the data.
A) y = 18.739 + 11.383 ln x C) y = 13.235 + 14.128 ln x
B) y = 15.381 + 12.590 ln x D) y = 10.546 + 13.533 ln x
Ans: A Section: 5.4

90. Use the regression model to estimate the persons total weight loss after 54 days.
A) 24.3 pounds B) 25.5 pounds C) 26.7 pounds D) 28.1 pounds
Ans: C Section: 5.4

91. According to the regression model, what is the projected weight loss for 97 days?
A) 33.3 pounds B) 35.6 pounds C) 37.2 pounds D) 37.8 pounds
Ans: A Section: 5.4

92. Solve. Round your answer to three decimal places.
10x = 32.8
A) 1.516 B) 3.28 C) 3.490 D) 328
Ans: A Section: 5.5

93. Solve. Round your answer to three decimal places.
e3x 2 + 30 = 180
Ans: 2.337
Section: 5.5

94. Solve. Round your answer to three decimal places.
10x 10 4 = 0.603
Ans: 4.220
Section: 5.5

95. Solve exactly.
log(3x 5) = 2
A) B) C) 35 D) 34
Ans: C Section: 5.5

96. Solve exactly.
log 20 + log x = 3
Ans: 50
Section: 5.5

97. Solve exactly.
log (x + 4) log (x 3) = log 8
Ans: 4
Section: 5.5

98. Solve. Round your answer to three decimal places.
30 = 1.09x
A) 39.467 B) 27.523 C) 3.401 D) 13.268
Ans: A Section: 5.5

99. Solve. Round your answer to three decimal places.
e3.7x + 35 = 0
A) 0.961 B) 0.961 C) 9.459 D) No solution
Ans: D Section: 5.5

100. Solve. Round your answer to three decimal places.
157 = 768e0.58x
A) 2.737 B) 0.352 C) 0.352 D) No solution
Ans: A Section: 5.5

101. Solve exactly.
ln(7x + 2) = ln(5x + 14)
Ans: 6
Section: 5.5

102. Solve exactly.
log(x + 20) log(x + 2) = log x
A) 5, 4 B) 4 C) 5 D) No solution
Ans: B Section: 5.5

103. Solve exactly.
(ln x)3 = ln x9
Ans: 1, e3, e3
Section: 5.5

104. Solve exactly.
9log x = 9x
A) B) C) D)
Ans: B Section: 5.5

105. If $7,000 is placed in an account with an annual interest rate of 3%, how long will it take the amount to double if the interest is compounded annually? Round your answer to two decimal places.
Ans: 23.45 years
Section: 5.5

106. If $4,000 is placed in an account with an annual interest rate of 5%, how long will it take the amount to triple if the interest is compounded annually? Round your answer to two decimal places.
A) 22.52 years B) 22.92 years C) 23.32 years D) 23.72 years
Ans: A Section: 5.5

107. What annual interest rate will ensure that $6,500 will grow to $9,000 if it is invested for 6 years with interest compounded continuously? Round your answer to two decimal places.
Ans: 5.42%
Section: 5.5

108. How many years will it take $3,500 to grow to $8,684 if it is invested at an annual rate of 2%, compounded continuously? Round your answer to one decimal place.
A) 44.4 years B) 44.9 years C) 45.4 years D) 45.9 years
Ans: C Section: 5.5

109. A mathematical model for population growth is given by P = P0ert where P is the population after t years, P0 is the population at t = 0, and the population is assumed to grow continuously at the annual rate r. How long would it take a population to triple if the growth rate were 2.4%? Round to one decimal place.
A) 45.8 years B) 46.3 years C) 46.8 years D) 47.3 years
Ans: A Section: 5.5

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