SOLUTION: 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 2000 fish. Abs

Question 1183428: 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 2000 fish. Absent constraints, the population would grow by 210% per year.
If the starting population is given by p0=500, 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 by Boreal(15235) (Show Source): You can put this solution on YOUR website!

Logistic equation is y=L/(1+be^(-kt)) and dP/dT=kP(1- (P/L))
L=2000, the carrying capacity.
k=constant of proportionality, or 2.1
Using the first,
t=0; 500=2000/(1+be^0)
500(1+b)=2000
b=3
t=1 season
y(1)=2000/(1+3e^(-2.1)=1462.66 or 1463
y(2)=2000/(1+3e^(-4.2))=1913.90 or 1914

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