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258 Chapter 3 Exponential and Logarithmic Functions<br />
23.<br />
fx <br />
10<br />
1 2e 0.05x 24.<br />
fx <br />
12<br />
1 4 x<br />
(a)<br />
12<br />
(a)<br />
2<br />
−12 12<br />
−100 100<br />
−2<br />
−14<br />
(b) Horizontal asymptotes: y 0, y 10<br />
(b) Horizontal asymptotes: y 0, y 12<br />
25. A Pe rt 10,000e 0.08t<br />
t 1 10 20 30 40 50<br />
A 10,832.87 22,255.41 49,530.32 110,231.76 245,325.30 545,981.50<br />
26. r 3% 0.03, A 10,000e 0.03t<br />
t 1 10 20 30 40 50<br />
A 10,305 13,499 18,221 24,596 33,201 44,817<br />
27.<br />
Vt 26,000 3 4 t 28.<br />
(a) 26,000<br />
Q 100 1 2 t14<br />
(a) When t 0, Q 100 grams.<br />
(b) When t 10, Q 100 1 2 1014 60.95 grams.<br />
(c)<br />
100<br />
0<br />
0<br />
15<br />
(b) For t 2, V2 $14,625.<br />
(c) The car depreciates most rapidly at the<br />
beginning, which is realistic.<br />
0<br />
0<br />
100<br />
29.<br />
33. ln e 4 4 34. lne 3 3 2 35. g6 lo4 3 64 36.<br />
37.<br />
41.<br />
log 5 125 3 30.<br />
e 4 e 4<br />
5 3 125<br />
25 32 125 38.<br />
log 25 125 3 2<br />
ln 1096.6331. . . 7<br />
e 32 e 3<br />
e 7 1096.6331. . . 42.<br />
log 6 36 2 31.<br />
6 2 36<br />
12 1 1 12<br />
39.<br />
log 12 12 1 1<br />
ln 0.0497. . . 3<br />
log 64 2 1 6 32.<br />
64 16 2<br />
log 4 64 3<br />
1 2 3 8 40.<br />
log 12 8 3<br />
e 3 0.0497. . . 43.<br />
log 10 100 1 2<br />
3 5 243<br />
log 3 243 5<br />
2 3 2 9 4<br />
log 23 9 4 2<br />
log 6 216 log 6 6 3<br />
10 2 1<br />
100<br />
3 log 6 6<br />
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3
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