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268 Chapter 3 Exponential and Logarithmic Functions<br />
156. ––CONTINUED––<br />
(b) Linear model: Quadratic model: Exponential model:<br />
3000<br />
3000<br />
3000<br />
0 15<br />
1500<br />
Logarithmic model:<br />
0 15<br />
1500<br />
Power model:<br />
0 15<br />
1500<br />
3000<br />
3000<br />
0 15<br />
1500<br />
0 15<br />
1500<br />
(c) The quadratic model is best because its coefficient of determination is closest to 1.<br />
(d) For 2010, t 20 and y 3015 thousand.<br />
(e) y 3000 when t 17.8, or 2007.<br />
157. (a)<br />
(b)<br />
P 9999.887<br />
1 19.0e 0.2x<br />
10,000<br />
0<br />
0<br />
36<br />
(c) The model is a good fit.<br />
(d) The limiting size is<br />
9999.887<br />
1 0 10,000<br />
fish.<br />
158. P 56.8e 0.001603t<br />
(a)<br />
Year 1990 1991 1992 1993 1994 1995<br />
P 56.8 56.9 57 57.1 57.2 57.3<br />
Year 1996 1997 1998 1999 2000 2001<br />
P 57.3 57.4 57.5 57.6 57.7 57.8<br />
Year 2002 2003 2004 2005<br />
P 57.9 58.0 58.1 58.2<br />
(b)<br />
Linear model<br />
(c) Slope is 0.09. The population increases by 90,000<br />
people each year.<br />
(d)<br />
y 56.8 0.09t 0<br />
58.5<br />
Slope <br />
58.2 56.8<br />
15 0<br />
y 0.09t 56.8,<br />
0 14<br />
56<br />
Answers will vary.<br />
0.09<br />
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