We saw that for a radioactive substance with half-life equal to T, the amount of the substance at time t is given by A(t) = A0e kt , where k = -ln(2/T).(a) Show that the probability that a radioactive particle decays after time t is given by (b) The book Atomic Adventures mentions that the mean life span of a

Chapter 10, Section 11.2 #44

We saw that for a radioactive substance with half-life equal to T, the amount of the substance at time t is given by A(t) = A0e^kt, where k = -ln(2/T).
(a) Show that the probability that a radioactive particle decays after time t is given by

(b) The book Atomic Adventures mentions that the mean life span of a muon is 1.44 times its half-life. Verify this fact by calculating the expected life of a particle with half-life T.