Yes, it's good
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