Exponential decay

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A = A_0 e^{-(t-t_0)/\tau}}

where $A_{0}$ is the value at time Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t_0} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau} expresses the rate of exponential decay. The quantity reaches one-half of its original value after a time interval equal to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tau} 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.

See also

• Exponential growth