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
 * $$\frac{dN}{dt} = \lambda N.$$
 * Exponential.svg

Proof
For a Differential Equation of the form
 * $$\frac{dN}{dt} = \lambda N.$$
 * $$\int \frac{dN}{N} = \lambda \int dt $$
 * $$ln N = \lambda t + c $$
 * $$N = e^( \lambda t + c) $$
 * $$N(t) = N_0 e^{\lambda t}. \,$$