Assume that in the absence of immigration and emigration, the growth of a countr

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 (see Equation (1) of Section 1.3). 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).)

dP 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 =

Explanation / Answer

1)

dP/dt = kP + r

2)

dP/dt = kP - r

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