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(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
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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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
Transcribed Image Text: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
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