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# Hubbert curve

The Hubbert curve, named after the geophysicist M. King Hubbert[?], is the derivative of the logistic curve.

An example of a Hubbert curve is:

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

The Hubbert curve closely resembles but is different from 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 be followed by a gradual decline of oil production to nothing.

Based on his model, Hubbert predicted (accurately) that, following from the peak of well discovery in 1948, oil production in the contiguous United States would peak in the late 1960s. According to this model, complete exhaustion of the U.S. oil reserves would then follow by the end of the 21st century.

Some people believe that if the Hubbert model is accurate, there are drastic implications for human culture and technological society, which is currently heavily dependent on oil as a fuel and chemical feedstock. Some of them envisage a Malthusian catastrophe occurring as the oil finally runs out.

However, the validity of this model is disputed by many geophysicists, and some economists believe that oil running out will lead to its replacement by other fuel sources and chemical feedstocks.

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