Algebra 2 CP
Chapter 7 Test Review
Name _____________________
Graph the following functions and determine the domain and range of the function. Also,
determine whether each function represents exponential growth or decay. Then, describe the
shifts from the parent function y = a∙bx.
x
1
1. y  2 
3
Growth / Decay
1 x
5
2
Growth / Decay
D = ______ R = ______
D = ______
Shifts:__________________
Shifts:__________________
4. y  3
Growth / Decay
1
5. y  3   1
3
Growth / Decay
D = ______ R = ______
D = ______
x3
2.
3. y  3e x
y
Growth / Decay
R = ______
D = ______
R = ______
Shifts:__________________
x2
1
Shifts:__________________
6. y  3e x  2  2
Growth / Decay
R = ______
Shifts:__________________
D = ______
R = ______
Shifts:__________________
7-9 Use the following information.
You deposit $2200 in an account that earns 3% annual interest. Find the balance after 15 years if the
interest is compounded with the given frequency. Round answers to the nearest cent.
7. monthly
8. quarterly
9. continuously
10. The population of a city can be modeled by P  125,000e0.02t where t is the number of years since
1990. What was the population in 1995?
11. You bought a motorcycle for $5800. It depreciates at a rate of 7.5% annually. If the motorcycle
is now worth $1200, how long ago did you buy it?
12-13 Use the following information.
You bought a CD for $15000. Four years later it was worth $22,525. Calculate the rate of interest
compounded with the given frequency.
12. Semi-annually
13. Continuously
14. You invest $1500 in a stock whose value has been increasing by approximately 5% per year.
The time required for an initial investment I0 to grow to I can be modeled where I0 and I are measured
I 
ln  
I0
in dollars and t is measured in years by the following equation: t   
0.049
a. How long before your investment doubles?
b. How long before your investment triples?
Rewrite the equation in exponential form.
15. log 10  1
18. log 25 125 
16. log 4
3
2
19.
1
 1
4
17. log 1 3  
9
ln 0.135  2
1
2
20. ln 20.086  3
Write each equation in logarithmic form.
23.
16
2
  
81
3
26.
e 3  1.948
5  125
22.
3
24.
e 4  54.598
25.
e 3  0.050
3
4
1

27
21.
3
2
Evaluate without a calculator.
27.
28. log 1 128
log 4 64
29. log 7
2
30.
33.
7
6x
25
7
2 x 5
2 x  20
 1 


 125 
y  ln x  3
1
 
8
31.
2
34.
ln e 3
x
32.
9 2 p 1  27 p  4
35.
e
x7
Find the inverse of the function.
y  log 15 x
36.
37.
39.
2 x 1
1
343
40.
ln 42
y  2  log 3 x  2
38.
y  log 4 x  3
y  ln x  1  1
41.
y  3  ln x  2
Graph the function and state its domain and range. Also, describe the horizontal and vertical
shifts from the parent function.
42. f x   log 3 x  2
43. f x  log 2 x  4
44. f x   ln x  1
D = _______ R = _______
D = _______
R = _______
Shifts:__________________
Shifts:__________________
D = _______ R = _______
Shifts:_______________
Expand the expression by rewriting.
45. log 4 5x
48.
log 6
5x3
6
46.
log 8 x 2
49.
ln
4
x2
Condense the expression by writing as a single logarithm.
log 3 4  log 3 y  3 log 3 x
2 log x  log  x  4 
51.
52.
x
4
47.
log 3
50.
ln
53.
2 ln x  4 ln 3  ln y
3x3
5
Use the Change-of-Base formula to evaluate. Round to the nearest thousandth.
log 7 12
log 5 1.25
54.
55.
56.
log 4 112
Use the approximate logarithms to evaluate the logarithm.
log 4  0.602
log 7  0.845
log 3  0.477
57.
log
5
4
58.
log 45
log 5  0.699
59.
log 105
Use log 12 3  0.442 and log 12 7  0.783 to approximate the value of each expression.
60.
log 12 21
61.
log 12 63
62.
log 12
7
3
Solve.
1
63  
9
x 3
 3x
64. 36 8 x 1  6 4 x 1
65. 4 x  2  16 x  4
66.
8 p  50
67.
8 y  4  15
68.
7.6 d 3  57.2
69.
log 6 2 x  6  log 6 x  2
70.
log 7 2  x   log 7 5 x
71.
log 3 x  2  log 3 3x 
72.
log 6 3 y  5  log 6 2 y  3
73. log 9 3u  14  log 9 5  log 9 2u
74.
4 log 2 x  log 2 5  log 2 405
77.
log b 3 
1
2
80. log 16 9 x  5  log 16 x 2  1 
83. 2e 3 x  5  2
86. ln 5x  ln 3x  9
1
2
log 2 4 x  4  5
76.
log 2 x  3
78. log 6 4 x  12  2
79.
log 10 4  log 10 w  2
81. e x 2  4  21
82. e 8 x  50
84. ln x  3  5  2
85. ln 5 x  3  3.6
75.
Write an exponential function y  ab x whose graph passes through the given points.
87. (1, 4) and (2, 16)
88. (2, 2) and (3, 1)
Use the table of values to create an exponential model that best fits the data.
89.
x
1
2
3
4
5
6
y
3.36
x
y
1
5.4
9.41
26.34 73.76 206.52 548.27
90.
2
9.72
3
4
5
6
17.496 31.493 56.687 102.04
Answer Key
1. Decay
D = (, )
R = (0, )
None
4. Growth
7. $3448.35
D = (, )
R = (1, )
Left 3, Down 1
8. $3444.50
2. Growth
5. Decay
D = (, )
R = (0, )
None
D = (, )
R = (1,  )
Right 2, Up 1
9. $3450.29
3. Growth
D = (, )
R = (0, )
None
6.
D = (, )
R = (2, )
Left 2, Down 2
Growth
10. 138, 146 people
11. 20.2 yrs
12. 10.4%
16. 4 1 
13. 10.2%
1
17.  
9
1
4
21. log 5 125  3
26. ln 1.948 
31. x =
2
3
1
5
36. y  15
41. y  e

1
2
14a. 14.1 years
3
3
1
 3
27
2
19. e  0.135
18. 25 2  125
16
4
81
3
3
20. e  20.086
23. log 2
24. ln 54.598  4
27. 3
28. -7
29. -3
30. x = -5
32. p = 14
33. x = 
34. 3
35. 42
22. log 3
x
2
37. y  3  2
x
1
15. 10  10
14b. 22.4 yrs
11
7
38. y  4  3
x
39. y  e
x 3
25. ln 0.050  3
40. y  e
x 1
1
x2
3
42. D = (2, )
R = (, )
Right 2
43. D = (0, )
R = (, )
Down 4
44. D = (0, )
R = (, )
Down 1
45. log 4 5  log 4 x
46. 2 log 8 x
47. log 3 x  log 3 4
48. log 6 5  3  log 6 x  1
49. ln 4  2 ln x
50. ln 3  3 ln x  ln 5
51. log 3 4 x 3 y
52. log
54. 1.277
55. 3.404
56. 0.139
57. 0.097
58. 1.653
59. 2.021
60. 1.225
61. 1.667
62. 0.341
63. x = -2
64. x = ¼
65. x = 10
66. p = 1.881
67. y = -2.698
68. d = -1.005
69. x = 6
70. x =
72. y = 8
73. u = 2
74. x = 3
75. x = 9
76. x = 8
77. b = 9
78. x = 6
79. w = 25
80. x = 3
81. x ≈ 4.833
82. x ≈ -0.489
83. No Solution
84. x ≈ 17.086
85. x ≈ 6.720
86. x ≈ 23.242
87. y  4
53. ln
x2 y
81
1
88. y  8   
2
x
89. y  1.2  2.8
x
1
3
x2
x4
71. x = 1
90. y  3  1.8
x
x