Answer to Question #268891 in Calculus for Xixo

Question

5. A model that describes the population P(t) of a fishery in which harvesting takes place at a constant rate is given by d = kph where k and h are positive constants. dP dt

(a) Solve the DE subject to P(0) = Po

(b) Describe the behavior of the population P(t) for increasing time in the three cases for Po >/, Po = /2 and 0 < Po < 1/1

(c) Use the results from part (b) to determine whether the fish population will ever go extinct in finite time, that is, whether there exists a time T> 0 such that P(T) = 0. If the population goes extinct, then find T.