A model that describes the population of a fi­shery in which harvesting takes place at a constant rate is given by

dP/dt = kP - h,

where k and h are positive constants.

(a) Solve the DE subject to P(0) = P₀.

(b) Describe the behavior of the population P(t) for increasing time in the three cases P₀ > h/k, P₀ = h/k, and 0 < P₀ < h/k.

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