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Section 3.5 Exponential and Logarithmic Models 243
15.
ln 3 rt
ln 3
r
3 e rt
t
r 2% 4% 6% 8% 10% 12%
t ln 3
r
60
54.93 27.47 18.31 13.73 10.99 9.16
3P Pe rt 0
0
0.14
16.
ln 3
3P P1 r t r 2% 4% 6% 8% 10% 12%
3 1 r t
ln 3 ln1 r t
ln 3 t ln1 r
t ln 3
ln1 r
60
55.48 28.01 18.85 14.27 11.53 9.69
ln1 r t 0
0
0.14
17.
2 18.
2
0
0
10
0
0
10
Continuous compounding results in faster growth.
A 1 0.075t
and A e 0.07t
A 1 0.06t
A 1 0.055
365 365t
From the graph, 5 1 2 % compounded daily
grows faster than 6% simple interest.
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19.
1
2 C Cek1599 20.
1
2 e1599k
k ln12
1599
y Ce kt
10e ln1215991000
6.48 g
1
2 C Cek1599 21.
1
2 e1599k
k ln12
1599
y Ce kt
1.5 Ce ln1215991000
1.5 C0.64824
C 2.31 g
1
2 C Cek5715
1
2 e5715k
k ln12
5715
y Ce kt
3e ln1257151000
2.66 g