Biologists stocked a lake with300fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be7500. The number of fish doubled in the first year.

(a) Assuming that the size of the fish population satisfies the logistic equation

dP/dt=kP (1PK),

determine the constantk, and then solve the equation to find an expression for the size of the population aftertyears.

k= __________________,

P(t)=________________.

(b) How long will it take for the population to increase to3750(half of the carrying capacity)?

It will take_________________________ years.