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# dp/dt = p^2 + p 10/3 where p is the number of frogs at time t years, and is a positive constant. (a) Determine the equilibrium solutions.

dp/dt = −p^2 + αp −10α/3

where p is the number of frogs at time t years, and α is a positive constant.

(a) Determine the equilibrium solutions.

>> after letting dp/dt =0, do i use the formula x=(-b +/- ((b^2-4ac)^0.5)/2a) to find the equilibrium solution of p in terms of α? If not how else should i solve it?

(b) For what values of α does the population model have one, two or no equilibrium solutions?

>> i have totally no idea how to approach this question.

Much help appreciated

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#### Top Answer

Hi, please find... View the full answer

a) For equilibrium, it’s correct that dp/dt should be made equal to zero.
Now, we arrive at the following expression:
−p^2 + αp −10α/3 = 0
This can be solved for p but the answer would be...

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