Consider a prolific breed of rabbits whose birth and death rates, β and δ, are each propor...

Consider a prolific breed of rabbits whose birth and death rates, β and δ, are each proportional to the rabbit population P = P(t), with β > δ.

(a) Show that

k constant Note that P(t) → + ∞ as t → l/(kP0). This is doomsday.

(b) Suppose that P0 = 6 and that there are nine rabbits after ten months. When does doomsday occur?