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
 * $$\frac{dN}{dt} = -\lambda N.$$
 * Plot-exponential-decay.svg

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