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= .

A)

B) P(t→∞)=2000

C)

Step-by-step explanation:

Given differential eq is

                      --- (1)

Eq is separable

                      --- (2)

substituting in  (2)

Integrating both sides

Back substituting value of u

---(3)

at t =0

from (3)

B)

which is the carrying capacity.

C) To find the fastest growth rate we have to maximize

From given differential eq

so function to maximize is

To maximize find f'(P)=0

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