On average the females in an insect population lay 6000 eggs

On average, the females in an insect population lay 6000 eggs and 3000 of the eggs are female eggs. The females in the insect population die when they lay their eggs. The fraction of female eggs that end up surviving long enough to reproduce is f. If the initial population of female insects is 250, write a different equation for the population of female insects. What is the range of f in which the female population stabilizes?

Solution

initial population

P(0) = 250

fP is the female population able to reproduce

fP * (3000) is added at each step

So dP/dt = fP*3000

P = constant * e^(3000f t)

where constant = 250 = P(0)