Applications of Differential Equations

Population Growth

Populations tend to have a growth rate proportional to the present popluation. This is true whether we’re talking about a the population of a country or a colony of bacteria or a herd of deer.

If we call the population, P, we can write this as a differential equation:

dP/dt = kP

where k is the constant of proportionality. This constant k is a function of societial factors for the growth of a human population, but we can determine it if we have information about previous growth rates. Let’s work a problem.

Problem: The population of a certain country is 2 million and has doubled in the last 20 years. Find the expected population in 80 years.

First summarize the given information: