Exponential Growth

In a basic, simple model of exponential growth, the time that a resource is depleted by a population depends on three variables: the available amount of the resource, the amount of the resource consumed per person, and the number of people in the population. If both the per capita consumption and the population grow exponentially, the time until depletion is a function of the two rates and the available amount of the resource (typically the initial amount).

The world currently has remaining between 80 and 90 times the amount of fossil fuels it currently produces in a year (for the high end, see BP’s latest estimates). Between 1980 and 2004, the population grew at about 1.5 percent per year and fuel production per person grew at less than one tenth of a percent per year (actually 0.07). With these rates, we will deplete all of our fossil fuels in less than 60 years (assuming that all fossil fuels are equal, which is the best case). If instead we had available 1,000 times our annual production (over 11 times the known amount), depletion would take only about 180 years. A massive one million times our annual production would be depleted in 620 years.

Total energy production, which includes fossil fuels, renewable sources, and nuclear energy, is growing over three times as fast as fossil fuel production alone, at about one-quarter of a percent per year (actually 0.24). At this rate, we would use up 1,000 times our current annual production in about 170 years and one million times our production in less than 570 years.

The global ecological footprint, which my more complex consumption model assumes is proportional to annual consumption of all natural resources, has historically grown on a per capita basis at an exponential rate close to the average of the rates for fossil fuel and total world energy (again for the period 1980-2004). Unlike energy production, the per capita rate for the ecological footprint is rapidly increasing, a trend which started around 1995. It has now reached a value about 11 times higher than its long term value (it is currently near two percent). If, like fossil fuels, we have 80-90 times as many resources available as we annually use now, then at two percent growth we will deplete our resources in about 40 years, corresponding to the time that my consumption model projects the world’s population will crash.