11: Section 4.1 Answers

1. \(Q=20e^{-(t\ln 2)/3200}\)

2. \(\frac{2\ln 10}{\ln 2}\text{days}\)

3. \(\tau = 10\frac{\ln 2}{\ln 4/3}\text{minutes}\)

4. \(\tau\frac{\ln (p_{0}/p_{1})}{\ln 2}\)

5. \(\frac{t_{p}}{t_{q}}=\frac{\ln p}{\ln q}\)

6. \(k=\frac{1}{t_{2}-t_{1}}\ln \frac{Q_{1}}{Q_{2}}\)

7. \(20\text{ g}\)

8. \(\frac{50\ln 2}{3}\text{yrs}\)

9. \(\frac{25}{2}\ln 2%\)

10. a. \(=20\ln 3\text{yr}\)
b. \(Q_{0}=100000e^{-5}\)

11. a. \(Q(t)=5000-4750e^{-t/10}\)
b. \(5000\text{lbs}\)

12. \(\frac{1}{25}\text{ yrs}\)

13. \(V=V_{0}e^{t\ln 10/2} \: 4\text{ hours}\)

14. \(\frac{1500\ln \frac{4}{3}}{\ln 2}\text{yrs};\quad 2^{-4/3}Q_{0}\)

15. \(W(t)=20-19e^{-t/20};\quad \lim_{t\to\infty }W(t)=20\text{ ounces}\)

16. \(S(t)=10(1+e^{-t/10});\quad \lim_{t\to\infty}S(t)=10\text{ g}\)

17. \(10\text{ gallons}\)

18. \(V (t) = 15000 + 10000e ^{t/20}\)

19. \(W(t) = 4 × 10^{6} (t + 1)^{2}\) dollars \(t\) years from now

20. \(p=\frac{100}{25-24e^{-t/2}}\)

21. \(p(t)={1000\over 1+999e^{-.9906t}}\) and \(p(6)=276\) people

22. \(5769\) fish

23. \(1400\) monkeys

24. \(1185\) otters

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