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Section 3.5 Exponential and Logarithmic Models 249
53.
t 10 ln
T 70
98.6 70
At 9:00 A.M. we have
t 10 ln 85.7 7098.6 70 6 hours.
Thus, we can conclude that the person died 6 hours
before 9 A.M., or 3:00 A.M.
54. t 5.05 ln
T (t 0 is 11 A.M.)
0 40
7 5.05 ln
T 40
0 40
7
5.05 ln T 40
40
T 40
40 e75.05
T 40 40e 75.05 29.998 30 < 32
Hence, the steaks do not thaw out in time.
55. False. The domain could be all real numbers.
56. False. See Example 5, page 380.
57. True. For the Gaussian model, y > 0.
58. True. See page 379.
59.
4x 3y 9 0 ⇒ y 1 3 4x 9
4
3
Slope:
Matches (a).
Intercepts: 0, 3, 9 4 , 0
60. Line with intercepts 5, 0 and 0, 2.
Matches (b).
61.
y 25 2.25x
Slope: 2.25
Matches (d).
Intercepts: 0, 25, 100
9 , 0
62. Line with intercepts 2, 0 and 0, 4.
Matches (c).
63.
f x 2x 3 3x 2 x 1
64.
f x 4x 4 x 2 5
The graph falls to the left and rises to the right.
Falls to the left and falls to right
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65.
67.
gx 1.6x 5 4x 2 2
The graph rises to the left and falls to the right.
4 2
2
8
8
0
3
0
3
2x 3 8x 2 3x 9
x 4
69. Answers will vary.
9
12
3
2x 2 3 3
x 4
66.
68.
gx 7x 6 9.1x 5 3.2x 4 25x 3
Rises to left and rises to right
5 1
1
0
5
5
x 4 3x 1
x 5
0
25
25
3
125
128
1
640
641
x 3 5x 2 25x 128 641
x 5