PS:Please solve c) correctly as I got my answer incorrect all the time.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= clndtPPwhere 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) = 4000e^(-(In(40/3)e^(-0.15t))(b) Compute the limiting value of the size of the population.lim P(t) = 4000(c) At what value of P does P grow fastest?P = 300

Given differential equation is dPdt=0.15ln4000PP To find the value of P at which P grow fastest.

(2) dP K cln P dt P 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) = | 4000e^(-(In(40/3)e^(-0.15t)) (b) Compute the limiting value of the size of the population. lim P(t) = 4000 (c) At what value of P does P grow fastest? P = 300

(2) dP K cln P dt P 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) = | 4000e^(-(In(40/3)e^(-0.15t)) (b) Compute the limiting value of the size of the population. lim P(t) = 4000 (c) At what value of P does P grow fastest? P = 300

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

PS:Please solve c) correctly as I got my answer incorrect all the time.

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
P
P
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) = 4000e^(-(In(40/3)e^(-0.15t))
(b) Compute the limiting value of the size of the population.
lim P(t) = 4000
(c) At what value of P does P grow fastest?
P = 300

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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