Arithmetic Course/Non Linear Function/Exponential function/Exponential decay

From Wikibooks, open books for an open world
Jump to: navigation, search

Exponential decay[edit]

Exponential decay function is a function that has the value decay exponentially

N(t) = N_0 e^{-\lambda t}. \,

Which can be proven as the root of a Differential Equation of the form

\frac{dN}{dt} = -\lambda N.
Plot-exponential-decay.svg

Proof[edit]

For a Differential Equation of the form

\frac{dN}{dt} = -\lambda N.
\int \frac{dN}{N} = -\lambda \int dt
ln N = -\lambda t + c
N = e^( -\lambda t + c)
N(t) = N_0 e^{-\lambda t}. \,