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. Then the rate of change of the population at time t is modeled by the differential equation dP/dt = kP-m where k= α - β. a. What condition on m will result in a constant popula tion? A population decline?b. Find the solution of this equation that satisfies the initial condition P(0) = P0. (Write an equation involving P, P0, k, m, and t.)