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## anonymous 3 years ago Differential equation question; if dp/dt = P-kP where P is population of rabbits. In a certain year the population is too high and they decide to shoot "S" rabbits each year. Therefore dp/dt = P-kP - S. Find in terms P and k the maximum amount of rabbits that can be shot each year to make the population stable.

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1. anonymous

$dp/p=(1-k)dt$ ----> $\ln p=(1-k)t + c$ equation of population before shooting after shooting ln p=(1-k-s)t + k ...differentiate it, get expression of s and equate it to zero to get the answer

2. anonymous

So do i equate dp/dt to 0?

3. anonymous

$1/p=1-k-s$

4. anonymous

sorry for previous reply...dont do dp/dt but get expression of s and do ds/dt

5. anonymous

OK thanks

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