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 K In (5) P =cln where c is a constant and K is the carrying capacity. a) Solve this differential equation for c = 0.15, K = 3000, and initial population Po = 200. P(t) =

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Chapter2: Second-order Linear Odes
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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
- In (A) P
=cln
where c is a constant and K is the carrying capacity.
(a) Solve this differential equation for c = : 0.15, K = 3000, and initial population Po = 200.
P(t) = ||
(b) Compute the limiting value of the size of the population.
lim P(t) =
1→∞
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 differential equation dP dt - In (A) P =cln where c is a constant and K is the carrying capacity. (a) Solve this differential equation for c = : 0.15, K = 3000, and initial population Po = 200. P(t) = || (b) Compute the limiting value of the size of the population. lim P(t) = 1→∞
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