Another model for a growth function for a limited population is given by the Gompertz function, which is a solution to the differential equation dPdt=cln(KP)P where c is a constant and K is the carrying capacity. Answer the following questions.

a. Solve the differential equation with a constant c=0.1, carrying capacity K=3000, and initial population P0=1000. P(t)=
(b) Compute the limiting value of the size of the population. limt→[infinity]P(t)= .(c) At what value of P does P grow fastest? P= .