Hubbert curve

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

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

The Hubbert curve has some resemblance to, but is different from, the shape of the probability density function of the normal distribution. It was popularised 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.

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