dP K cln P dt P nere c is a constant and K is the carrying capacity. Solve this differential equation for c = 0.15, K = 4000, and initial population Po = 300. (t) = O Compute the limiting value of the size of the population. m P(t) = At what value of P does P grow fastest?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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PS:Please answer a) to c) correctly

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
cln
dt
where c is a constant and K is the carrying capacity.
(a) Solve this differential equation for c = 0.15, K = 4000, and initial population Po = 300.
P(t) =
(b) Compute the limiting value of the size of the population.
lim P(t) =
(c) At what value of P does Pgrow fastest?
P =
Transcribed Image Text:() dP cln dt where c is a constant and K is the carrying capacity. (a) Solve this differential equation for c = 0.15, K = 4000, and initial population Po = 300. P(t) = (b) Compute the limiting value of the size of the population. lim P(t) = (c) At what value of P does Pgrow fastest? P =
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