An individual disposes of 13 unwanted pet goldfish in a small lake. After 8 months, there are 25...

Question

An individual disposes of 13 unwanted pet goldfish in a small lake. After 8 months, there are 25 goldfish in the lake.

(a) Write a differential equation for the population P assuming logistic growth, where the lake can support at most 100 goldfish. Use A for the growth parameter.

dPdt =

(b) Find the specific solution P(t) for the population of goldfish as a function of t .

P(t)=

David · Accepted Answer

A) 
The logistic differential equation is written as: 
P'(t) = r P(t) [1 - P(t)/K].  
 dP/dt = r P [1 - P / K] 
We can use A as the growth parameter and K=100 which is the capacity 
dP/dt = AP [1 - P / 100] 
B) 
To solve the logistic differential equation, we separate variables:

An individual disposes of 13 unwanted pet goldfish in a small lake. After 8 months, there are 25 goldfish in the lake. (a) Write a differential equation for the population P assuming logistic growth,...

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