Download File
Download File
Download File
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
266 Chapter 3 Exponential and Logarithmic Functions<br />
1<br />
145. P 361e kt<br />
146.<br />
2 P Pek245,500<br />
t 0 corresponds to 2000.<br />
ln<br />
20, 215:<br />
<br />
1<br />
ln 2<br />
245,500k ⇒ k <br />
2 245,500<br />
215 361e k20<br />
2.8234 10 6<br />
215<br />
361 After 5000 years,<br />
e20k<br />
A e k5000 0.98598 or 98.6% remains.<br />
20k ln <br />
215<br />
361<br />
k 1<br />
20 ln 215<br />
361 1<br />
20 ln 361<br />
215 0.02591<br />
P 361e 0.02591t<br />
For 2020, P20 361e 0.0259120 606.1 or<br />
606,100 population in 2020.<br />
147. (a) 20,000 10,000e r12 148. (a) 0.1<br />
2 e 12r<br />
ln 2 12r<br />
r ln 2<br />
12<br />
0.0578 or 5.78%<br />
(b) 10,000e 0.05781 $10,595.03<br />
0 150<br />
0<br />
y 0.0499e x742 128<br />
(b) The average score corresponds to the<br />
maximum, 74.<br />
149. (a)<br />
50 <br />
1 5.4e 0.12t 158<br />
50<br />
5.4e 0.12t 108<br />
50<br />
e 0.12t 108<br />
505.4<br />
0.12t ln 108<br />
270<br />
158<br />
1 5.4e 0.12t (b) Similarly:<br />
t ln108270<br />
0.12<br />
150. R log 10 I<br />
I 0<br />
log 10I ⇒ I 10 R<br />
(a)<br />
(b)<br />
I 10 8.4 251,188,643<br />
I 10 6.85 7,079,458<br />
7.6 weeks<br />
75 <br />
1 5.4e 0.12t 158<br />
75<br />
158<br />
1 5.4e 0.12t<br />
e 0.12t 0.20494<br />
0.12t ln0.20494<br />
t 13.2 weeks<br />
© Houghton Mifflin Company. All rights reserved.<br />
(c) I 10 9.1 1,258,925,412
Change language