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Question Assume there is certain population of fish in pond whose growth described by the logistic equation_ estimated that the carrying capacity for the pond 1800 ...

Question

Question Assume there is certain population of fish in pond whose growth described by the logistic equation_ estimated that the carrying capacity for the pond 1800 fish _ Absent constraints the population would grow by 1207 per year. the starting population given by Po 300_ then after one breeding season the population of the pond given by Alter two breeding seasons the population of the pond given by Question Help: Dvideo Qvideo Submit Questlon

Question Assume there is certain population of fish in pond whose growth described by the logistic equation_ estimated that the carrying capacity for the pond 1800 fish _ Absent constraints the population would grow by 1207 per year. the starting population given by Po 300_ then after one breeding season the population of the pond given by Alter two breeding seasons the population of the pond given by Question Help: Dvideo Qvideo Submit Questlon



Answers

The fish population in a pond with carrying capacity 1000 is modeled by the logistic equation
$$
\frac{d N}{d t}=\frac{.4}{1000} N(1000-N)
$$
Here, $N(t)$ denotes the number of fish at time $t$ in years. When the number of fish reached $275,$ the owner of the pond decided to remove 75 fish per year.
(a) Modify the differential equation to model the population of fish from the time it reached $275 .$
(b) Plot several solution curves of the new equation, including the solution curve with $N(0)=275.$
(c) Is the practice of catching 75 fish per year sustainable, or will it deplete the fish population in the pond? Will the size of the fish population ever come close to the carrying capacity of the pond?


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