Consider a population P = P(t) with constant relative birth and death rates and β, respectively, and a constant emigration rate m, where , β, and m are positive constants. Assume that > β. Then the rate of change of the population at time t is modeled by the differential equation dP dt = kP − m where k = − β. (a) Find the solution of this equation that satisfies the initial condition P(0) = P0. (Write an equation involving P, P0, k, m, and t.)