# Exponential decay

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A quantity is said to be subject to **exponential decay** if it decreases at a rate proportional to its value. Symbolically, this can be expressed as the following differential equation, where *N* is the quantity and λ is a positive number called the decay constant.

The solution to this equation (see below for derivation) is:

Here *N(t)* is the quantity at time *t*, and *N _{0} = N(0)* is the initial quantity, i.e. the quantity at time

*t = 0*.

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