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Section 3.4 Solving Exponential and Logarithmic Equations 237<br />
132. (a)<br />
(b)<br />
2000 1000e 0.06t 133. (a)<br />
2 e 0.06t<br />
ln 2 0.06t<br />
t ln 2 11.55 years<br />
0.06<br />
3000 1000e 0.06t<br />
3 e 0.06t<br />
ln 3 0.06t<br />
t ln 3 18.31 years<br />
0.06<br />
(b)<br />
2000 1000e 0.025t<br />
2 e 0.025t<br />
ln 2 0.025t<br />
t ln 2 27.73 years<br />
0.025<br />
3000 1000e 0.025t<br />
3 e 0.025t<br />
ln 3 0.025t<br />
t ln 3 43.94 years<br />
0.025<br />
134. (a)<br />
136.<br />
(b)<br />
2000 1000e 0.0375t 135.<br />
2 e 0.0375t<br />
ln 2 0.0375t<br />
t ln 2 18.48 years<br />
0.0375<br />
3000 1000e 0.0375t<br />
3 e 0.0375t<br />
ln 3 0.0375t<br />
p 5000 1 <br />
t ln 3 29.30 years<br />
0.0375<br />
4<br />
p 500 0.5e 0.004x <br />
(a)<br />
(b)<br />
p 350<br />
350 500 0.5e 0.004x <br />
300 e 0.004x<br />
0.004x ln 300<br />
x 1426 units<br />
p 300<br />
300 500 0.5e 0.004x <br />
400 e 0.004x<br />
0.004x ln 400<br />
x 1498 units<br />
© Houghton Mifflin Company. All rights reserved.<br />
0.002x 4 e<br />
(a) When p $600:<br />
(b) When p $400:<br />
600 5000 1 <br />
0.12 1 <br />
4<br />
0.88<br />
0.002x<br />
4 e<br />
4 3.52 0.88e 0.002x<br />
0.48 0.88e 0.002x<br />
6<br />
11 e0.002x<br />
ln 6 ln e0.002x<br />
11<br />
ln 6 11 0.002x<br />
x ln611<br />
0.002<br />
4<br />
4 e 0.002x<br />
4<br />
4 e 0.002x<br />
303 units<br />
400 5000 1 <br />
0.08 1 <br />
4<br />
0.92<br />
4 e0.002x 4 3.68 0.92e 0.002x<br />
0.32 0.92e 0.002x<br />
8<br />
23 e0.002x<br />
ln 8 ln e0.002x<br />
23<br />
x ln823<br />
0.002<br />
4<br />
4 e 0.002x<br />
4<br />
4 e 0.002x<br />
528 units
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