United States Elementary Differential Equations - 1st Order Differential Equations

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1. The problem statement, all variables and given/known data

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.

2. Relevant equations



3. 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.

vela

I think that's a typo. It should be -100.