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240 Chapter 3 Exponential and Logarithmic Functions
147. Yes. The doubling time is given by
2P Pe rt
2 e rt
ln 2 rt
t ln 2
r .
The time to quadruple is given by
4P Pe rt
4 e rt
ln 4 rt
t ln 4
r
ln 22
r
which is twice as long.
2 ln 2
r
2
ln 2
r
148. To find the length of time it takes for an
investment P to double to 2P, solve
2P Pe rt
ln 2 rt
ln 2
r
2 e rt
t.
Thus, you can see that the time is not dependent
on the size of the investment, but rather the
interest rate.
149. f x 3x 3 4
y
2
1
−4 −3 −2 −1
−1
2 3 4
−2
−3
x
150.
f x x 1 3 2
151.
f x x 9
y
y
5
4
3
18
15
1
−5 −4 −3 −2 −1
−1
1 2 3
−2
−3
x
9
6
3
−9 −6 −3
−3
3 6 9 12
−6
x
152.
f x x 2 8 154. 153.
y
y
y
16
12
5
8
8
4
4
4
3
x
2
−4
−12 −4 8 12 16
−4
1
x
−4 −3 −2 −1 1 3 4
−8
−12
−16
−3
−16
f x
2x,
x 2 4,
x < 0
x ≥ 0
fx
x 9,
x 2 1,
−12 −8
4 8 12
−4
x ≤ 1
x > 1
x
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