Question

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.

Answer 1

\[dp/p=(1-k)dt\] ----> \[\ln p=(1-k)t + c\] 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

Answer 2

So do i equate dp/dt to 0?

Answer 3

\[1/p=1-k-s\]

Answer 4

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

Answer 5

OK thanks