How fast will Resource X be depleted?
Well suppose we have the following situation:
Congressperson says "oh don't worry, Resource X will be around for 100 years"
Really .... don't we use resources like rabbits?
70/n years; n =% growth rate
Its important to recognize that even in the slow growth period, the use of the resource is exponential. If you fail to realize that, you will run out of the resource pretty fast.
The correct equation for calculating the exponential exhaustion timescale of any resource (should be required knowledge for any one elected to congress):
where k = growth rate
R = total resource available
ro = initial consumption rate
Let's start out with the curve for US Oil production. Note that peak production occurs on a timescale of 1/2 of Te as the production curve is assumed to be symmetric. When resources reach peak production, prices tend to go up which can then serve to lower consumption and extend the exhaustion timescale.
In 1956, M. King Hubbert published an ignored paper based on this methodology as applied to US Oil production.
Other Examples to do in the Excel Template
Top 10 World Resource Usage (in units of millions of short tons per year - year 2005)
Back to Congress:
The basic problem is that we substitute Disney's First Law for this arithmatic reality of resource depletion.