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 Bo births per month and Dq deaths per month are occurring at time t = 0, show that the limiting population is M = B0P0/D0.
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