Consider a rabbit population P(t) satisfying the logistic equationas in Problem 15. If the initial population is 120 rabbits thereare 8 births per month and 6 deaths per month occurring at timet=0, how many months does it take for P(t) to reach 95% of thelimiting population M?
What problem 15 says since you need to know:
Consider a population P(t) satisfying the logistic equation
dp/dt = aP –bP²
, where B=aP is the time rate at which births occur and D=bP² is the rate at which deaths occur. If the initial population is P(0) = P₀, and B₀ births per month and D₀ deaths per monthare occurring at time t=0, show that the limiting population is M =B₀P₀/D₀.
