Please need an answer asap

I correct. Another model for a growth function for a limited population is given by the Gompertz function, which is a solution of the differential equation dP dt = cln (pP where c is a constant and K is the carrying capacity. (a) Solve this differential equation for c - 0.2, K = 3000, and initial population Po = 500. 3000 P(t) = pe -0.21 + In(In 6) (b) Compute the limiting value of the size of the population. lim P(t) = 1-+00 (c) At what value of P does P grow fastest? 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 3000. The number of fish doubled in the first year. (a) Assuming that the size of the fish population satisfies the logistic equation dP at = KP (1 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 1500 (half of the carrying capacity)? It will take years