Another model for a growth function for a limited population is given by the gompertz function, which is a solution of the differential equation dpdt=cln(kp)p where c is a constant and k is the carrying capacity.(a) solve this differential equation for c=0.1, k=2000, and initial population p0=500. 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= .