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:







d
N


d
t



=
−
λ
N
.


{\displaystyle {\frac {dN}{dt}}=-\lambda N.}
The solution to this equation (see derivation below) is:




N
(
t
)
=

N

0



e

−
λ
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, rate constant, or transformation constant.

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