Logistic growth Fish Pond

Question

Assume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1600 fish. Absent constraints, the population would grow by 230% per year.

   

If the starting population is given by , then after one breeding season the population of the pond is given by

P1 =

After two breeding seasons the population of the pond is given by

P2

Answer 1

This is a growth problem and and will utilize the following formula:

A=P(1+r)^y

A=200(1+2.3)^1 for the first year A = 660 fish

A=200(1+2.3)^2 for the second year A=2178, However Given the lakes capacity of 1600 fish, it will not reach this amount. It will reach capacity during the second year and be at 1600.