Shell Oil scientist M. King Hubbert made a remarkable prediction in 1956. He had analyzed the depletion patterns of various natural resources, and proposed that the production rates of a given resource from a given region would tend to follow a roughly bell-shaped curve. More specifically, he used what is now called the “Hubbert curve”, which is a probability density function of a logistic distribution curve. This curve is like a gaussian function (which is used to plot normal distributions), but is somewhat “wider”:
Normalized Hubbert Curve. Source: Wikipedia.
Hubbert used various reasonable assumptions (which we will not canvass here) in formulating this model curve. Notably, it predicts that the peak production rate will occur when the total resource from that region is 50% depleted, and that the fall in production on the back side of the curve will be as fast as the rise in production…
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Utopia, you are standing in it! 
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