**Exponential Decay**

A model for decay of a quantity for which the rate of decay is directly proportional to the amount present. The equation for the model is A = A_{0}b^{t} (where 0 < *b* < 1 ) or A = A_{0}*e*^{kt} (where *k* is a negative number representing the rate of decay). In both formulas A_{0} is the original amount present at time *t* = 0.

This model is used for phenomena such as radioactivity or depreciation. For example, A = 50*e*^{–0.01t} is a model for exponential decay of 50 grams of a radioactive element that decays at a rate of 1% per year.

**See also**

Exponential growth, half-life, continuously compounded interest, logistic growth, *e*

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