# Hubbert curve

The Hubbert curve, named after the geophysicist M. King Hubbert, is the derivative of the logistic function.

An example of a Hubbert curve is:

$x = {e^{-t}\over(1+e^{-t})^2}={1\over2+2\cosh t}$

The Hubbert curve closely resembles, but is different from, the shape of the probability density function of the normal distribution. It was originally intended as a model of the rate of petroleum extraction. According to this model, the rate of production of oil is determined by the rate of new oil well discovery; a "Hubbert peak" in the oil extraction rate will thus be followed by a gradual decline of oil production, to nothing.

For more information on petroleum exhaustion, see the Hubbert peak theory article.