Consider a population P$($t$)$P$($t$)$ of rabbits living in a region with unlimited food resources. Suppose that the growth rate is proportional to the population with a proportionality factor of $33$ per month. Suppose that every month we hunt HH rabbits.

$($a$)$ Write the differential equation P$=$f$($P$)$P$=$f$($P$)$ satisfied by the rabbit population.

f$($P$)=$f$($P$)=$

functions

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Note: Type P for P$($t$)$P$($t$)$ and H for HH$.$

$($b$)$ Find the equilibrium solutions for this equation. If there is more than one solution write them separated by commas.

Equilibrium Solutions: