Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for thefish of that species in that lake) to be 4600. The number of fish doubled in the first year.(a) Assuming that the size of the fish population satisfies the logistic equationP(1-).dP= kP ( 1dtKdetermine the constant k, and then solve the equation to find an expression for the size of the population after tyears.kP(t) =(b) How long will it take for the population to increase to 2300 (half of the carrying capacity)?It will takeyears.

Biologists stocked a lake with 500 fish and estimated the carrying capacity (the maximal population for th fish of that species in that lake) to be 4600. The number of fish doubled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP = kP ( 1 - dt p(1-) determine the constant k, and then solve the equation to find an expression for the size of the population after t years. k = P(t) = (b) How long will it take for the population to increase to 2300 (half of the carrying capacity)? It will take years.