1. x(t)=22−e−t
2. x(t)=101+9e−10t
3. x(t)=2+e−2t2−e−2t
4. x(t)=3(1−e−12t)2(1+e−12t)
5. x(t)=408−3e−15t
6. x(t)=102+3e15t
7. x(t)=7711−4e−28t
8. x(t)=22117−4e91t
9. 484
10. 20 weeks
11. (b) P(t)=(12t+10)2
12. P(t)=24020−t
13. P(t)=18030−t
14. P(t)=P01+kP0t
16. About 27.69 months
17. About 44.22 months
19. About 24.41 months
20. About 42.12 months
21. 2001+e−6/5≈153.7 million
22. About 34.66 days
23. (a) limt→∞ x(t)=200 grams (b) 54ln 3≈1.37 seconds
24. About 9.24 days
25. (a) M=100 and k=0.0002; (b) In the year 2075
26. 50 ln 98≈15.89 months
27. (a) 100 ln95≈58.78 months; (b) 100 ln 2≈69.31 months.
28. (a) The alligators eventually die out.(b) Doomsday occurs after about 9 years 2 months.
29. (a) P(140)≈127.008 million (b) About 210.544 million; (c) In 2000 we get P≈196.169, whereas the actual 2000 population was about 281.422 million.
31. a≈0.3915; 2.15×106 cells
37. k≈0.0000668717, M≈338.027
38. k≈0.000146679, M≈208.250
39. P(t)=P0exp(kt+b2πsin 2 πt); the colored curve in the figure below shows the graph with P0=100, k=0.03, and b=0.06. It oscillates about the black curve which represents natural growth with P0=100 and k=0.03. We see that the two agree at the end of each full year.