Assume that in the absence of immigration and emigration the growth of a country s population P t satisfies dP dt KP for some constant k 0 see Equation 1 of Section 1 3 Determine differential equation governing the growing population P t of the country when individuals are allowed to immigrate into the country at a constant rate r 0 Use P for P t dP X dt What is the differential equation for the population P t of the country when individuals are allowed to emigrate at a constant rate r 0 dP dt X