Chapter 5.1, Problem 54E

Time Constant and Half-life Consider as exponential decay function $P\left(t\right)=P_0{e}^{-\lambda t}$, and let $T$ denote its time constant. Show that, at $t=T$, the function $P\left(t\right)$ decays to about one-third of its initial size. Conclude that the time constant is always larger than the half-life.