Exponential decay is the decrease in a quantity according to the law

for a parameter and constant (known as the decay constant), where is the exponential function and is the initial value. Exponential decay is common in physical processes such as radioactive decay, cooling in a draft (i.e., by forced convection), and so on. Exponential decay is described by the first-order ordinary differential equation

which can be rearranged to

Integrating both sides then gives

and exponentiating both sides yields the functional form (1).

See also

Damped Exponential Cosine Integral, Exponential Function, Exponential Growth, Malthusian Parameter, Population Growth

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Cite this as:

Weisstein, Eric W. "Exponential Decay." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ExponentialDecay.html

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