Question

Biologists stocked a lake with 240 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6,000. The number of fish tripled in the first year.

(a) Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.

P=_____

(b) How long will it take for the population to increase to 3000? (Round your answer to two decimal places.)
_____yr

Please show all work neatly, line by line, and please justify each step so that I can learn,

Thank you!

Answer 1

PART(a):

The solution of the logistic Differential equation is given by,

where M is the maximum carrying capacity,

A is the integration const.

k is rate constant.

we need to find A and k based on the information given.

put t = 0,

Now the solution becomes,

put t = 1,

solving for k,

Now the final solution becomes,

PART(b):

solving for t,

I hope this answer helps,
Thanks,
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