Exponential decay

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, disintegration constant,^[1] rate constant,^[2] or transformation constant:^[3]

${\displaystyle {\frac {dN(t)}{dt}}=-\lambda N(t).}$

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

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

where N(t) is the quantity at time t, N₀ = N(0) is the initial quantity, that is, the quantity at time t = 0.