Exponential decay

Exponential decay is the decay of a physical property whose value goes as

$A=A_{0}e^{-(t-t_{0})/\tau }$

where $A_{0}$ is the value at time $t_{0}$ and $\tau$ expresses the rate of exponential decay. The quantity reaches one-half of its original value after a time interval equal to $\tau$ ln 2, which is called its half-life.