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#### alane1994

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- Oct 16, 2012

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**Suppose that the population of a species of fish in a certain lake is hypothesized to grow according to a logistic model of population growth with growth rate \(r=0.3\) and carrying capacity \(k=3000\). Assume initially there are 2500 fish of the species in the lake. Determine the correct differential equation for each of the scenarios below.**

(a) Each year 150 fish are harvested from the lake.

(b) Each year 25% of the fish are harvested from the lake.

(c) What is a maximum (within 50) safe fixed amount to harvest each year in order to assure that there will always be some fish in the lake.

(a) Each year 150 fish are harvested from the lake.

(b) Each year 25% of the fish are harvested from the lake.

(c) What is a maximum (within 50) safe fixed amount to harvest each year in order to assure that there will always be some fish in the lake.

Now I am looking and re-reading in my book, but I am rather confused by this. I am reading in the section entitled "Autonomous Equations and Population Dynamics".