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

Exponential decay

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

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

Proof

For a Differential Equation of the form

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

$\int {\frac {dN}{N}}=-\lambda \int dt$

$lnN=-\lambda t+c$

$N=e^{(}-\lambda t+c)$

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