where <math>A_0</math> is the value at time <math>t_0</math> and <math>\tau</math> expresses the rate of exponential decay. The quantity reaches one-half of its original value after a time interval equal to <math>\tau</math> ln 2, which is called its [[half-life]]. | where <math>A_0</math> is the value at time <math>t_0</math> and <math>\tau</math> expresses the rate of exponential decay. The quantity reaches one-half of its original value after a time interval equal to <math>\tau</math> ln 2, which is called its [[half-life]]. |