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

Exponential Growth

Exponential Growth function is a function that has the value growth 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

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

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

$lnN=\lambda t+c$

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

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