9.4 Differential Equations
Population Growth Model: Overview
Differential equation can be used to model population growth based on the law of natural growth,
logistic equation and a few other applications.
The Law of Natural Growth
Assumption: population grows at a rate proportional to the population size: , where ( ) is the
value of at time , and is a constant. For , population increases; for , population
Taking integral of both sides of the differential equati∫n: ∫ ; , where
representing an arbitrary constant. Thus, ( ) , meaning the initial population.
Rewriting the equation means the relative growth rate is co