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).