# Exponential decay

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

$A = A_0 e^{-(t-t_0)/\tau}$

where A0 is the value at time t0 and τ expresses the rate of exponential decay. The quantity reaches one-half of its original value after a time interval equal to τ ln 2, which is called its half-life.

## Examples

Examples of exponential decay include the radioactive decay of radioisotopes, the attenuation of sound or light through an absorber, and the decay of the magnetic fields of the planets.[1]