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. a. 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.
b. 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?

Step-by-step explanation:

Given

Solving (a): Differential equation for immigration where

We have:

Make dP the subject

From the question, we understand that: . This means that

--- i.e. the population will increase with time

Divide both sides by dt

Solving (b): Differential equation for emigration where

We have:

Make dP the subject

From the question, we understand that: . This means that

--- i.e. the population will decrease with time

Divide both sides by dt

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