When a radioactive substance decays, the fraction of atoms present at time t is (t) = e

When a radioactive substance decays, the fraction of atoms present at time t is ƒ(t) = e^−kt, where k > 0 is the decay constant. It can be shown that the average life of an atom (until it decays) is A = − ∫ ^∞₀ t ƒ(t) dt. Use Integration by Parts to show that A = ∫^∞₀ ƒ(t) dt and compute A. What is the average decay time of radon-222, whose half-life is 3.825 days?