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

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Exponential Growth[edit]

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.
Exponential.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}. \,