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238 Chapter 3 Exponential and Logarithmic Functions<br />
137.<br />
7247 596.5 ln t 5800<br />
596.5 ln t 1447<br />
ln t 2.4258<br />
t 11.3, or 2001<br />
138.<br />
V 6.7e 48.1t , t > 0<br />
(a)<br />
10<br />
(c)<br />
1.3 6.7e 48.1t<br />
1.3<br />
6.7 e48.1t<br />
0<br />
0<br />
1500<br />
(b) As t → , V → 6.7.<br />
Horizontal asymptote: y 6.7<br />
The yield will approach<br />
6.7 million cubic feet per acre.<br />
ln 13<br />
67 48.1<br />
t<br />
t 48.1 29.3 years<br />
ln 1367<br />
139. (a)<br />
110<br />
140.<br />
P 0.83<br />
1 e 0.2n<br />
f<br />
m<br />
(a)<br />
1<br />
0<br />
0<br />
110<br />
(b) From the graph we see horizontal asymptotes at<br />
y 0 and y 100. These represent the lower and<br />
upper percent bounds.<br />
(c) Males:<br />
1 e 0.6114x69.71 2<br />
0.6114x 69.71 ln 1<br />
0.6114x 69.71 0<br />
Females:<br />
50 <br />
e 0.6114x69.71 1<br />
50 <br />
1 e 0.66607x64.51 2<br />
e 0.66607x64.51 1<br />
0.66607x 64.51 ln 1<br />
0.66607x 64.51 0<br />
100<br />
1 e 0.6114x69.71<br />
x 69.71 inches<br />
100<br />
1 e 0.66607x64.51<br />
x 64.51 inches<br />
−40<br />
(b) Horizontal asymptotes: y 0, y 0.83<br />
The upper asymptote, y 0.83, indicates<br />
that the proportion of correct responses will<br />
approach 0.83 as the number of trials<br />
increases.<br />
(c) When P 60% or P 0.60:<br />
0.60 0.83<br />
1 e 0.2n<br />
1 e 0.2n 0.83<br />
0.60<br />
0<br />
40<br />
e 0.2n 0.83<br />
0.60 1<br />
ln e 0.2n ln <br />
0.83<br />
0.60 1 <br />
0.2n ln <br />
0.83<br />
0.60 1 <br />
0.83<br />
ln 0.60 1 <br />
n <br />
5 trials<br />
0.2<br />
© Houghton Mifflin Company. All rights reserved.
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