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242 Chapter 3 Exponential and Logarithmic Functions
t 21,
t 12,
9. Since A 7500e rt and A 15,000 when
10. Since A 1000e rt and A 2000 when we
15,000 7500e 21r 2000 1000e 12r
we have the following.
have the following.
2 e 21r
ln 2 21r
r ln 2
21
Amount after 10 years:
0.033 3.3%
A 7500e 0.03310 $10,432.26
2 e 12r
ln 2 12r
r ln 2
12
0.058 5.8%
Amount after 10 years:
A 1000e 0.05810 $1786.04
11. Since A 5000e rt and A 5665.74 when
t 10, we have the following.
5665.74 5000e 10r
5665.74
5000 e10r
ln
5665.74
5000 10r
The time to double is given by
10,000 5000e 0.0125t
2 e 0.0125t
ln 2 0.0125t
r 1 10 ln 5665.74
5000
0.0125 1.25%
t ln 2 55.5 years.
0.0125
12. Since A 300e rt and A 385.21 when
t 10, we have the following.
385.21 300e 10r
385.21
300 e10r
ln
385.21
300 10r
The time to double is given by
600 300e 0.025t
2 e 0.025t
ln 2 0.025t
r 1 10 ln 385.21
300
0.025 2.5%
t ln 2 27.7 years.
0.025
13. Since A Pe 0.045t and A 100,000 when t 10,
we have the following.
100,000 Pe 0.04510
100,000
e 0.45 P 63,762.82
The time to double is given by
127,525.64 63,762.82e 0.045t
2 e 0.045t
ln 2 0.045t
t ln 2 15.4 years.
0.045
14. Since A Pe 0.02t and A 2500 when t 10, we
have the following.
2500 Pe 0.0210
2500
P $2046.83
e0.02 The time to double is given by
4093.66 2046.83e 0.02t
2 e 0.02t
ln 2 0.02t
t ln 2 34.7 years.
0.02
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