Consider the differential equation as a model for a fish population, where is measured in weeks and

Question:

Consider the differential equation as a model for a fish population, where is measured in weeks and is a constant.

(a) Use a CAS to draw direction fields for various values of c.
(b) From your direction fields in part (a), determine the values of c for which there is at least one equilibrium solution. For what values of does the fish population always die out?
(c) Use the differential equation to prove what you discovered graphically in part (b).
(d) What would you recommend for a limit to the weekly catch of this fish population?