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Section 3.5 Exponential and Logarithmic Models 247<br />
39.<br />
pt <br />
1000<br />
(a)<br />
(b)<br />
1 9e 0.1656t 1000<br />
p5 <br />
animals<br />
1 9e0.16565 203<br />
(c)<br />
500 <br />
1 9e 0.1656 t 2<br />
9e 0.1656t 1<br />
e 0.1656t 1 9<br />
1000<br />
1 9e 0.1656t<br />
t ln19<br />
0.1656 13<br />
months<br />
1300<br />
0 100<br />
0<br />
The horizontal asymptotes are p 0 and<br />
p 1000. The population will approach 1000<br />
as time increases.<br />
40.<br />
y <br />
663<br />
© Houghton Mifflin Company. All rights reserved.<br />
1 72e 0.547t, 0 ≤ t ≤ 18<br />
(a) 1000<br />
(b) For t 19, y 662.<br />
For t 30, y 663.<br />
(c) As t →, y → 663 limiting value.<br />
0<br />
18<br />
0<br />
1 663,<br />
(d) Answers will vary.<br />
41. R log 10 I<br />
I 0<br />
log 10I ⇒ I 10 R<br />
42. R log 10 I<br />
I 0<br />
log 10I<br />
(a) I 10 6.1 1,258,925<br />
(a) R log 10 39,811,000 7.6<br />
(b) I 10 7.6 39,810,717<br />
(b) R log 10 12,589,000 7.1<br />
(c) I 10 9.0 1,000,000,000<br />
(c) R log 10 251,200 5.4<br />
43. I 10 log 10 II 0 , where I 0 10 12 watt per square meter.<br />
(a) 10 10 10 log 10 1010<br />
12 10 10 log 10 102 20 decibels<br />
(b) 10 5 10 log 10 105<br />
12 10 10 log 10 10 7 70 decibels<br />
(c) 10 0 10 log 10 100<br />
12 10 10 log 10 1012 120 decibels<br />
44.<br />
I 0<br />
10 log I<br />
10 12 10<br />
10 log 10 I<br />
(a) 10 4 10 log 10 104<br />
12 decibels<br />
10 10 log 1010 8 80<br />
(b) 10 3 90 decibels<br />
(c) 10 2 100 decibels
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