Growth and decay

Footnote

⁵Rigorously: Over a period beginning at a particular time \(t = t_0\) and ending at \(t = t_0 + T\), the term \(e^{kt}\) decreases from \(e^{k t_0}\) to \(e^{k(t_0 + T)} = e^{k t_0} e^{kT} = \dfrac{1}{2} e^{kt_0}\), that is, decreases by half.