Differential Equations

Study of equations involving derivatives and their applications.

Practical Applications

Modeling Population Growth

How Populations Change

Differential equations are used to predict how populations of animals, bacteria, or even people grow over time.

The Equation

\( \frac{dP}{dt} = rP \)

Where:

  • \( P \) is the population,
  • \( r \) is the growth rate.

What Can We Learn?

  • How fast a population can grow
  • When a population might reach a certain size

Examples

  • Predicting when a new species will overrun an island.

  • Estimating the spread of a virus in a city.

Modeling Population Growth - Differential Equations Content | Practice Hub