Question

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. Determine a 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).)

Answer 1

Answer:

dP/dt = kP+r

Step-by-step explanation:

We know 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. Therefore, we have differential equation:

dP/dt = kP .

If  individuals are allowed to immigrate into the country at a constant rate r > 0, we conclude that we have the differential equation  

dP/dt = kP+r .