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## Homework Statement

I only need help with problem 16 but included problem 15 because it is referenced in problem 16.

16.

Suppose that the growth-rate parameter k = 0.3 and the carrrying capacity N = 2500 in the logistic population model of Excercise 15. Suppose p(0) = 2500.

(a) If 100 fish are harvested each year, what does the model predict for the long term behavior of the fish population? In other words, what does a qualitative analysis of the model yield?

(b) If one-thrid of the firs are harvested each year, what does th emodel predict for the long-term behavior of the fish population?

15.

Suppose a species of fish in a paricular lake has a population that is modeled by the logistic opulation model with growth rate k, carrying capacity N, and time t measured in years. Adjust th emodel to account for each of the following situations.

(a) 100 fish are harvested each year.

(b) One-third of the firsh population is harvested annually.

(c) The number of fish harvested each year is proportional to the square root fo the number of fish in the lake.

## Homework Equations

## The Attempt at a Solution

16.

(a)

I thought that this would be the correct differential equation

dP/dt = 3/10(1-P/2500)-100

but I guess this is wrong because I found this question and answer here on google search

http://www.math.uga.edu/~azoff/courses/2700notes.pdf

and it claims that the correct equation is

dP/dt = 3/10(1-P/2500)-300

I'm not exactly sure as to why it's minus 300 and not minus 100

thanks for any help that anyone can provide.

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