Question: 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(K/P)P

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(K/P)P

where cis a constant and Kis the carrying capacity.

(a) Solve this differential equation for

c=0.2, K=1000, and initial population P0=100.

P(t)=.

(b) Compute the limiting value of the size of the population.

limtP(t)=.

(c) At what value of Pdoes Pgrow fastest?

P=.

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