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

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

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

$lnN=-\lambda t+c$

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

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