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Review Exercises for Chapter 3 265
134.
p 500 0.5e 0.004x
(a)
p 450
(b)
p 400
450 500 0.5e 0.004x
0.5e 0.004x 50
e 0.004x 100
0.004x ln 100
x 1151 units
400 500 0.5e 0.004x
0.5e 0.004x 100
e 0.004x 200
0.004x ln 200
x 1325 units
135.
y 3e 2x3 136. y 4e 2x3
137. y lnx 3
Decreasing exponential
Matches graph (e).
Intercept: 0, 4
Increasing
Matches (b).
Logarithmic function shifted
to left
Matches graph (f).
138.
y 7 logx 3
Vertical asymptote: x 3
Decreasing
139. y 2e x42 3
Gaussian model
Matches graph (a).
140.
Matches (d).
y
6
1 2e 2x
Logistic model
Matches (c).
141.
y ae bx
2 ae b0 ⇒ a 2
3 2e b4
1.5 e 4b
ln 1.5 4b ⇒ b 0.1014
Thus, y 2e 0.1014x. .
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142.
143.
y ae bx
2 ae b0 ⇒ a 2
1 2e b5 ⇒ 1 2 e5b ⇒ 5b ln 1 2 ⇒ b 1 5 ln 1 2 1 5 ln 2 0.1386
y 2e 0.1386x
y ae bx 144.
1
2 ae b0 ⇒ a 1 2
5 1 2 eb5
10 e 5b
ln 10 5b ⇒ b 0.4605
Thus, y 1 2 e0.4605x .
ln 1 8
y ae bx
4 ae b0 a ⇒ a 4
1
2 4eb5
1
8 e5b
5b ⇒ b ln
8
5 0.4159
⇒ y 4e 0.4159x