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 \(k <0 \).

E 6.2 Exercises