Consider a population P = P(t) with constant relative birth and death rates and , respectively, and a constant emigration rate m, where ,

Consider a population P = P(t) with constant relative birth and death rates α and β, respectively, and a constant emigration rate m, where α, β, and m are positive constants. Assume that α > β. The rate of change of the population at time t is modeled by the differential equation
dP / dt = kP - m where k = α - β