The fish population in a pond with carrying capacity 1000 is modeled by the logistic equation

Here, N(t) denotes the number of fish at time t in years. When the number of fish reached 275, the owner of the pond decided to remove 75 fish per year.

(a) Modify the differential equation to model the population of fish from the time it reached 275.

(b) Plot several solution curves of the new equation, including the solution curve with N(0) = 275.

(c) Is the practice of catching 75 fish per year sustainable, or will it deplete the fish population in the pond? Will the size of the fish population ever come close to the carrying capacity of the pond?

Transcribed Image Text:

dN dt .4 1000 -N(1000 - N).