When predicting population growth, demographers must consider birth

and death rates as well as the net change caused by the difference between

rates of immigration and emigration. Let P be the population at time t

and N be the net increase per unit time due to the difference between

immigration and emigration. The rate of growth for the population is

given by

dP/dt = kP + N

Solve the differential equation and find P as a function of time

I got P = (Ce^t - N)/K