Download - Answers to Algebra 2 Unit 4 Practice
A1© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice
Answers to Algebra 2 Unit 4 PracticeLeSSon 19-1 1. D
2. a. 24, 26, 28, 210, 212
b. 22, 0, 2, 4, 6
c. 23, 0, 3, 6, 9
3. a. 5
b. 4
c. 22
4. There is no common difference.
5. She is incorrect. The sequence is arithmetic with a common difference of 4. The next two terms are 23 and 27.
LeSSon 19-2 6. C
7. a. 299
b. 1057
c. 690
8. a. 2505
b. 5445
c. 8030
9. 50.05
10. a. 61
b. 257
c. 168
LeSSon 19-3 11. B
12. B
13. 222.5
14. 19
15. 211
LeSSon 20-1 16. neither
17. geometric, r 5 3
18. 49,152
19. False, the common ratio is 6: 14
(6) 5 64
, 64
(6) 5 9.
20. 4.71 meters
LeSSon 20-2 21. C
22. D
23. a. 2425
b. 243,688
c. 11.56
d. 2180
24. a. an 5 5n 1 1
b. 19,530
25. 8
LeSSon 20-3 26. C
27. a. 28
b. does not exist: r $ 1
c. does not exist: r $ 1
d. 100,000
28. a. diverges
b. converges
c. diverges
d. diverges
29. r 5 14
30. Tuscany’s mom is correct: 20 12n
n
0∑
=
∞
5 40.
A2© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice
LeSSon 21-1 31. The graph will be a straight line.
32. a. x 1 2 3 4 5
f (x) 2.7 4.5 6.3 8.1 9.9
b. f (x) 5 1.8x 1 0.9
33. A
34. a. yes
b. yes
c. yes
35. C
LeSSon 21-2 36. C
37. A
38. a. exponential, f (x) 5 4814
x
b. linear, f (x) 5 6x 1 2
c. neither ( f (x) 5 x2)
39. a. 66%
b. 0.66
c. x 5 {1, 2, 3, 4, 5, 6, 7, 8, 9}, f (x) 5 {30, 10, 3.33, 1.11, 0.37, 0.12, 0.03, 0.01, 0.005}; the domain is positive since they represent the number of purchases; Tony spends his last whole cent on the ninth purchase. (Some students may choose to include 0 in the domain and 90 in the range.)
40. f (x) 5 7.5 13
x
; decay function.
LeSSon 21-3 41. The graphs are the same because the functions
are equal: f(x) 5 13
x
5
13
x
x 5 13x 5 32x.
42. exponential function
43. D
44. a. (2∞, ∞); (0, ∞); increases; (0, 3)
b. (2∞, ∞); (0, ∞); decreases; (0, 5)
c. (2∞, ∞); (2∞, 0); increases; (0, 22)
d. (2∞, ∞); (2∞, 0); increases; (0, 21)
45. The function is decreasing for all a , 0.
LeSSon 21-4 46. reflection over the x-axis
47. a.
x
y
g(x) f(x)
25210
5
10
15
5 10
b. y 5 2
c. vertical stretch by factor of 2, reflection over the y-axis, vertical shift by 12
48. horizontal shift to the left by 4
49. vertical shift up by 4
50. for all a , 0
LeSSon 21-5 51. C
52. B
53. a 5 2 and a 5 3
54. a.
x
y
210 25
210
25
10
5
5 10
g(x)
f(x)
A3© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice
b. vertical stretch by factor of 3, vertical shift down by 2
c. domain (2∞, ∞), range (22, ∞), asymptote at y 5 22
55. g(x) 5 22.8(ex 2 4.2)
LeSSon 22-1 56. A magnitude 8.0 earthquake indicates 1000 times
the ground motion of a magnitude 5.0 earthquake.
57. Yes; an earthquake with a magnitude of 4.0 and lower will rarely cause damage. An earthquake with magnitude of 6.0 may cause some damage, but a magnitude of 8.0 is devastating.
58. No; a magnitude 0.0 earthquake indicates ground motion of 0.001 cm.
59. a. 631 times
b. 3981 times
c. 50,119 times
d. 12,589,254 times
60. between 4 and 5
LeSSon 22-2 61. a. magnitude 3.3
b. magnitude 4.4
c. magnitude 7.7
d. magnitude 9.8
62. a. log 1000 5 3
b. log 1,000,000 5 6
c. log 1100
5 22
d. log 1
10,000 5 24
63. a. 104 5 10,000
b. 102 5 100
c. 1024 5 1
10,000
d. 1027 5 1
10,000,000 64. a. n
b. b
65. D
LeSSon 22-3 66. a. log 5 1 log x
b. log 3 2 log y
c. 4 log x
d. 3 log m 2 log 4
67. a. 20.195
b. 0.195
c. 1.885
68. a. log yx
47
b. log xy
5
2
c. log xy44 3
d. log ab
69. C
70. log (5)(13) 5 log 5 1 log 13 5 1.8
LeSSon 22-4 71. No; by the Power and Product Properties,
log xy2 5 log x 2 2 log y.
72. Yes; log 10 5 log (5)(2) 5 log 5 1 log 2 and log mn 5 log (m)(n) 5 log m 1 log n.
73. The Quotient Property states that
log uy
2
5 5 log u2 2 log y5, and the Power Property
states that log u2 2 log y5 5 2 log u 2 5 log y.
74. a. log 10,000 5 4
b. log 1 5 0
c. log 10 5 1
75. C
LeSSon 23-1 76. D
77. a. x
b. x
c. y
A4© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice
78. x 5 3y 2 4,
x 1 4 5 3y,
y 5 x 431
,
f 21(x) 5 x 431
79. The line of symmetry between a function and its inverse is y 5 x.
80. a. g (x) 5 log14
(x)
b. g (x) 5 x 251
c. g (x) 5 x7
22
d. g (x) 5 log5 x
e. g (x) 5 ex
LeSSon 23-2 81. a. log5 125 5 3
b. log7 1343
5 23
c. log 1 5 0
d. log4 64 5 3
82. a. 34 5 81
b. 93 5 729
c. e0 5 1
d. 623 5 1216
83. 4
84. log1024 1 5 0; any number to the power of 0 is 1.
85. A
LeSSon 23-3 86.
x 22 21 0 1 2
f ( x) 5 3x19
13
1 3 9
87. x
19
13 1 3 9
g A4 (x) 5 log3 x 22 21 0 1 2
88.
x
y
210 25
210
25
10
5
5 10
(0, 1)
f (x)
g(x)
(1, 0)
89. f(x) 5 3x : domain (2∞, ∞), range (0, ∞)
g(x) 5 log3 x: domain (0, ∞), range (2∞, ∞)
90. B
LeSSon 24-1 91. C
92. a. x 5 2
b. x 5 2
c. x 5 43
d. x 5 23
93. a. x 5 158
b. x 5 2
c. x 5 34
d. x 5 32
94. 15
ln 3
95. 13
ln 26
LeSSon 24-2 96. D
97. A
A5© 2015 College Board. All rights reserved SpringBoard Algebra 2, Unit 4 Practice
98. a. x ≈ 4
b. x ≈ 3
c. x ≈ 2
d. x ≈ 3
99. a. x 5 3.907
b. x 5 3.170
c. x 5 2.154
d. x = 2.912
100. x 5 1.105
LeSSon 24-3 101. A
102. B
103. a. x 5 6
b. x 5 223
c. x 5 27
d. x 5 26
104. a. x 5 9
b. x 5 227
c. x 5 113
d. no solution
105. a. (4, ∞)
b. (25, ∞)
c. (4.5, ∞)
d. (223
, ∞)
LeSSon 24-4 106. B
107. a. x $ 397.164
b. 1.667 , x # 14.937
c. x $ 0.546
108.
x
y
23 22 21
23
22
21
2
3
4
1
5
1 2 3 4 5
(3.75, 3.42)
0 # x # 3.75
109. x . 1.410
110. 2.333 , x # 3.861