MATH 2412 Quiz No. 5 Name: ___________________________
Fall 2017 due Thursday, September 28, 2017
SHOW ALL WORK FOR FULL CREDIT.
From #20 (p.404) Assume that W(t) denotes the amount of radioactive material in a substance at time t. Radioactive decay is then described by the differential equation , where λ is a positive constant called the decay constant.
1) Give the solution to , i.e., W(t) = ____________.
2) Assume that W(0) = 123 g and W(5) = 20 g and that time is measured in minutes. Find the decay constant λ.
From #22 (p.404) Denote by L(t) the length of a fish at time t, and assume that the fish grows according to the von Bertalanffy equation .
1) Give the solution to . (Use separation of variables technique, IF YOU WANT, or use formula 8.21 from book, p. 396).
2) Use your solution in (a) to determine k under the assumption that L(4) = 10. Sketch the graph of L(t) for this value of k.
3) Find the asymptotic length of the fish; that is, find