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Section 3.2 Logarithmic Functions and Their Graphs 211
89.
fx ln x 90.
fx ln x 2
(a)
3
(a)
7
−1 5
−1 11
−1
−1
(b)
ln x ≥ 0 ⇒ x ≥ 1;
Domain: x ≥ 1
(c) The graph is increasing on 1, .
(d) There are no relative maximum or
relative minimum values.
(b) Domain: x > 0
(c) The graph is decreasing on 0, 1 and
increasing on 1, .
(d) Relative minimum: 1, 0
91.
f t 80 17 log 10 t 1, 0 ≤ t ≤ 12
(a)
(b)
f 0 80 17 log 10 0 1 80
f 4 80 17 log 10 4 1 68.1
(c) f 10 80 17 log 10 10 1 62.3
(d) 100
0
0
12
92. (a)
360
0
140
110
The model is a good fit.
(b) T > 300F when p > 67.3 pounds per square
inch
The graph of T and y 300 intersect at
p 67.3.
(c) T74 306.48F
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93.
95.
t ln K
0.055
(a)
K 1 2 4 6 8 10 12
t 0 12.6 25.2 32.6 37.8 41.9 45.2
As the amount increases, the time increases,
but at a lesser rate.
(b)
60
−5
−10
10 log 10
(a)
I
10 12
20
94. (a)
I 1: 10 log 10
1
12 10 10 log 1010 12 1012 120 decibels
(b) I 10 2 : 10 log 10 102
12 10 10 log 1010 10 1010 100 decibels
(c) No, this is a logarithmic scale.
(b)
r 0.005 0.010 0.015
t 138.6 yr 69.3 yr 46.2 yr
The doubling time decreases as r increases.
200
0
0
r 0.020 0.025 0.030
t 34.7 yr 27.7 yr 23.1 yr
0.50