Test Bank for College Algebra 8th Edition by Ziegler, Byleen Barnett

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College Algebra 8th Edition by Ziegler, Byleen Barnett -Test Bank

 

Sample  Questions

 

Chapter 5

 

1. Evaluate  to four significant digits.

Ans:  22.27

Section:  5.1

 

2. Evaluate e⁹ – e^–9 to four significant digits.
3. A) 8103    B)  8107    C)  8111    D)  8115

Ans:  A     Section:  5.1

 

3. Simplify.

(4^7x)^10y

Ans:  4^70xy

Section:  5.1

 

4. Graph y = 4e^x.

Ans:

Section:  5.1

 

5. Graph y = 5e^–x.
6. A)                          C)
7. B)                          D)

Ans:  B     Section:  5.1

 

6. Find the equations of any horizontal asymptotes without graphing.

y = + 8

1. 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 = e^x – 7

Ans:  y = –7

Section:  5.1

 

8. Graph y = e^x – 3.

Ans:

Section:  5.1

 

9. Graph y = e^{x – 2}.
10. A)                          C)
11. B)                          D)

Ans:  D     Section:  5.1

 

10. Solve.

5^6x = 5^{2x + 8}

Ans:  2

Section:  5.1

 

11. Solve.

 

1. A) 3    B)  4    C)  5    D)  –4

Ans:  C     Section:  5.1

 

12. Solve.

= 1000

Ans:

Section:  5.1

 

13. Solve.

            x²e^x + 4xe^x = 0

1. A) 0    B)  –4    C)  0, 4    D)  0, –4

Ans:  D     Section:  5.1

 

14. Solve the exponential equation.

100^{x – 3}  = 1000^x

Ans:  –6

Section:  5.1

 

15. Graph .

Ans:

Section:  5.1

 

16. Graph .

Ans:

Section:  5.1

 

17. Graph f(x) = e^{x + 2} – 3.

Ans:

Section:  5.1

 

18. Simplify.

 

1. A)     B)      C)      D)

Ans:  D     Section:  5.1

 

19. Simplify.

 

1. 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?
21. 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(2^t/7.8)

Section:  5.2

 

24. How many bacteria will the culture contain after 4 hours?
25. 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.
27. A) 30,000,000 people                                 C)      32,000,000 people
28. 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.
28. A) 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.
30. A) 121 million people                                 C)      123 million people
31. 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 = 70e^–0.0025t.

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 = I₀e^–0.028d

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.
33. 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 = ab^x 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.
38. A)                               C)
39. B)                              D)

Ans:  D     Section:  5.2

 

38. Use the model to find the approximate value of y when x = 55.
39. 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

1. A) 0001 = 10^–4                                         C)      10 = (0.0001)^–4
2. B) 0001 = (–4)¹⁰                                      D)      10 = (–4)^0.0001

Ans:  A     Section:  5.3

 

42. Write in exponential form:

 

Ans:   = 5^–2

Section:  5.3

 

43. Write in exponential form.

 

Ans:   = 16^–1/2

Section:  5.3

 

44. Write in logarithmic form.

243 = 3⁵

1. 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.

= 25^–3/2

Ans:

Section:  5.3

 

47. Write in logarithmic form.

= 4^–2

Ans:

Section:  5.3

 

48. Simplify.

log ₄ 1

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

1. A) 0    B)  1    C)  3    D)  9

Ans:  B     Section:  5.3

 

51. Simplify.

log ₂ 2⁷

1. 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

1. A)     B)      C)  2     D)  –2

Ans:  C     Section:  5.3

 

54. Simplify.

log ₂

1. A)     B)      C)  5     D)  –5

Ans:  D     Section:  5.3

 

55. Simplify.

 

1. 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.
58. A) 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.
60. A) 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

1. A) 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

1. 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
71. A)     B)  –1    C)      D)

Ans:  B     Section:  5.3

 

71. Given that  and  find .
72. 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)

1. A)

 

1. B)

 

1. C)

 

1. 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) = 8^x

Section:  5.3

 

77. Find f ^–1 if f(x) = 2log ₈ (x – 3).
78. A) f ^–1(x) = 8^2x – 3                                       C)      f ^–1(x) = 8^x/2 – 3
79. B) f ^–1(x) = 8^2x + 3                                       D)      f ^–1(x) = 8^x/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 = 10^–12 watts per square meter.

 

79. A rock concert has a volume with an intensity of I = 1.0 ´ 10^–1 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 ´ 10^–6 W/m².  Find its rating in decibels to two significant digits.
81. 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 = 10^4.40 joules.

 

81. An earthquake has an energy release of 4.93 ´ 10⁸ joules.  What was its magnitude on the Richter scale?
82. A) 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, W_t is the takeoff weight (fuel, structure, and payload), and W_b is the burnout weight (structure and payload).

 

83. A rocket has a weight ratio W_t/W_b = 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.
84. A) 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 W_t/W_b = 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 pHH 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 ´ 10^–8.

 

85. Find the pH of the solution.  Round your answer to one decimal place.
86. A) 3      B)  8.4    C)  8.5    D)  8.6

Ans:  B     Section:  5.4

 

86. Is the solution acidic or basic?
87. 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 ´ 10^–3.

 

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?
89. 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.
90. A) y = –18.739 + 11.383 ln x                     C)      y = –13.235 + 14.128 ln x
91. 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 person’s total weight loss after 54 days.
91. A) 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?
92. A) 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.

10^x = 32.8

1. A) 516    B)  3.28    C)  3.490    D)  328

Ans:  A     Section:  5.5

 

93. Solve.  Round your answer to three decimal places.

e^{3x – 2} + 30 = 180

Ans:  2.337

Section:  5.5

 

94. Solve.  Round your answer to three decimal places.

10^–x 10 ⁴ = 0.603

Ans:  4.220

Section:  5.5

 

95. Solve exactly.

log(3x – 5) = 2

1. 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 = 1.09^x

39. A) 467    B)  27.523    C)  3.401    D)  13.268

Ans:  A     Section:  5.5

 

99. Solve.  Round your answer to three decimal places.

e^–3.7x + 35 = 0

1. A) –0.961    B)  961    C)  9.459    D)  No solution

Ans:  D     Section:  5.5

 

100. Solve.  Round your answer to three decimal places.

157 = 768e^–0.58x

2. A) 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

1. 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, e^–3

Section:  5.5

 

104. Solve exactly.

9^{log x} = 9x

1. 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.
107. A) 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.
109. A) 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 = P₀e^rt 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.
110. A) 8 years    B)  46.3 years    C)  46.8 years    D)  47.3 years

Ans:  A     Section:  5.5