Another model for a growth function for a limited population is given by the Gompertz function, which is a solution of the diferential equation dP -cln dt where c is a constant and K is the carrying capacity. (a) Solve this differential equation for e- 0.25, K = 4000, and initial population A= 400. P(t) = (b) Compute the limiting value of the size of the population lim P(t) = t00 (c) At what value of P does P grow fastest?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Another model for a growth function for a limited population is given by the Gompertz function, which is a solution of the ditferential equation
dP
-cln
dt
K
where c is a constant and K is the carrying capacity.
(a) Solve this differential equation for c = 0.25, K = 4000, and initial population A = 400.
P(t) =
(b) Compute the limiting value of the size of the population.
lim P(t) =
t00
(c) At what value of P does P grow fastest?
P =
Transcribed Image Text:Another model for a growth function for a limited population is given by the Gompertz function, which is a solution of the ditferential equation dP -cln dt K where c is a constant and K is the carrying capacity. (a) Solve this differential equation for c = 0.25, K = 4000, and initial population A = 400. P(t) = (b) Compute the limiting value of the size of the population. lim P(t) = t00 (c) At what value of P does P grow fastest? P =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,