Question

under the same assumptions underlying the model in (1), determine a differential equation for the population P(t) of a country when individuals are allowed to immigrate into the country at a constant rate r>0. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate from the country at a constant rate r>0?

Answer 1

When there is no immigration and emigration in a country, the differential equation of growth of population, P(t) satisfies the model

$\frac{dP}{dt}=kP,$ for some constant k > 0.

(I) When individuals are allowed to immigrate at constant rate r > 0, the differential equation will be

$\frac{dP}{dt}=kP + r$

(ii) When individuals are allowed to emigrate at constant rate r > 0, the differential equation will be

$\frac{dP}{dt}=kP - r$