# 6.2 | Differential Equations: Growth and Decay

Exponential Growth and Decay Model
If $$y$$ is a differentiable function of $$t$$ such that $$y >0$$ and $$y’ = k y$$ for some constant $$k$$, then
$$y = C e^{kt}$$
where $$C$$ is the initial value of $$y$$, and $$k$$ is the proportionality constant. Exponential growth occurs when $$k>0$$, and exponential decay occurs when $$k <0$$.