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).)

Question

Mathematics

Aria Ortega

15 January, 15:35

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).)

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Kiara Pearson · Answer 1

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.