Expii

# Differential Equations for Exponential Growth and Decay - Expii

We revisit exponential growth and decay from the perspective of differential equations: namely, the exponential differential equation, $$y' = ky$$, where $$k$$ is a constant (sometimes called the relative growth constant). The general solution is $$y(t) = ce^{kt}$$, which exhibits exponential growth when $$k$$ is positive, exponential decay when $$k$$ is negative, and neither whether $$k=0$$. Here $$c = y(0)$$ is determined by the initial conditions (or sometimes other data).