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