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

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 is modeled by the differential equation dP/dt = KP – m where k = α – β.
(a) Find the solution of this equation that satisfies the initial condition P (0) = P0.
(b) What condition on m will lead to an exponential expansion of the population?
(c) What condition on m will result in a constant population?
A population decline?
(d) In 1847, the population of Ireland was about 8 million and the difference between the relative birth and death rates was 1.6% of the population. Because of the potato famine in the 1840s and 1850s, about 210,000 inhabitants per year emigrated from Ireland. Was the population expanding or declining at that time?