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

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