Half-life \(t_{1/2}\) and mean life \(\tau\) are related by: \(t_{1/2} = \tau \ln 2 = 0.693\,\tau\). Since \(t_{1/2} = 0.693\,\tau\), they are directly proportional to each other (one is always a fixed constant times the other). The half-life is always shorter than the mean life by a factor of \(\ln 2\).