Sustainability and the Use of Non Renewable Resource, Australia as an Example

A government minister in Australia writes that Australian coal will last ``110 years at present rates of production.'' (1) But production is growing 5\% per year, so the life expectancy will be less than 110 y. Assume production follows a Gaussian Hubbert curve. We can construct a family of curves for the future path of P(t) vs. t, each of which is consistent with the 110 y. This envelope of this family of curves divides the graph of P(t) vs. t into allowed and forbidden areas. The curve with the current value of dP/dt is then the most probable future path of P(t). The curve reaches a maximum and then rapidly declines to zero. Australia's growing population and these Hubbert curves combine to indicate frightening non-sustainability. Sustainability requires a curve of P(t) that declines exponentially with k = (1/110) per y.(2) \newline (1) Ian Macfarlane, World Energy, V.8, 112-117, 2005 \newline (2) A.A. Bartlett, Am.J.Phys., V.54, 398-402, 1986