(Solved):   Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal p ...

 

Biologists stocked a lake with 300 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 5700 . The number of fish tripled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation \[ \frac{d P}{d t}=k P\left(1-\frac{P}{K}\right) \] determine the constant \( k \), and then solve the equation to find an expression for the size of the population after \( t \) years: \[ \begin{array}{l} k=\square \\ P(t)= \end{array} \] (b) How long will it take for the population to increase to 2850 (half of the carrying capacity)? It will take years.