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Section 3.1 Exponential Functions and Their Graphs 199<br />
45.<br />
f x <br />
8<br />
(a)<br />
1 e 0.5x 11<br />
(b)<br />
x 30 20 10 0 10 20 30<br />
f x<br />
0<br />
0<br />
0.05 4 7.95 8 8<br />
−9<br />
9<br />
Horizontal asymptotes: y 0, y 8<br />
−1<br />
46. (a)<br />
10<br />
(b)<br />
x<br />
15<br />
2<br />
1<br />
0.2<br />
0.1<br />
f x<br />
3.93 3.5 3.0 0.61 0.05<br />
−9<br />
9<br />
−2<br />
x 0 0.01 0.2 1 5<br />
f x<br />
undef. 8 7.4 5.0 4.2<br />
Horizontal asymptote:<br />
y 4<br />
Vertical asymptote: x 0<br />
47.<br />
f x <br />
6<br />
(a)<br />
2 e 0.2x 10<br />
(b)<br />
x 20 10 0 3 3.4 3.46<br />
−15<br />
15<br />
f x<br />
3.03<br />
3.22<br />
6<br />
34<br />
230<br />
2617<br />
−10<br />
x 3.47 4 5 10 20<br />
f x 3516 26.6 8.4 1.11 0.11<br />
Horizontal asymptotes: y 3, y 0<br />
Vertical asymptote: x 3.47<br />
48. (a)<br />
10<br />
49.<br />
2000<br />
© Houghton Mifflin Company. All rights reserved.<br />
(b)<br />
−9<br />
x<br />
f x<br />
−2<br />
Asymptotes:<br />
9<br />
15 10 1 0.1 0.01<br />
5.9 5.9 5.1 3.2 3<br />
x<br />
0.2<br />
ln 2<br />
0.289 1 4 10<br />
f x undef. 2715 7.7 6.3 6.1<br />
y 6<br />
x 0.2<br />
ln 2 0.2885<br />
0 100<br />
0<br />
Intersection: 86.350, 1500
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