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Exponential decay

Exponential decay

Probability density

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant:

{\displaystyle {\frac {dN}{dt}}=-\lambda N.}{\frac {dN}{dt}}=-\lambda N.

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

{\displaystyle N(t)=N_{0}e^{-\lambda t},}{\displaystyle N(t)=N_{0}e^{-\lambda t},}

where N(t) is the quantity at time t, N0 = N(0) is the initial quantity, that is, the quantity at time t = 0, and the constant λ is called the decay constant, disintegration constant,[1] rate constant,[2] or transformation constant.

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