# Math Insight

### Exponential growth and decay modeled by continuous dynamical systems

#### Video

Exponential growth and decay in continuous dynamical systems.

#### Question

For the differential equation \begin{align*} \diff{x}{t} &= rx\\ x(0) &= x_0, \end{align*} what is the condition for the solution to exhibit exponential growth?

What is the condition for the solution to exhibit exponential decay?