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