1) Initial production of conventional oil was 0, and final oil production will be 0, since there is a finite amount of oil to extract.
2) Annual production in between the initial and final numbers will be a positive number, and if you made a graph where the x-axis is the year and the y-axis is that year's production, the area under the resultant curve--whatever shape it may be--would be the ultimately recoverable oil.
3) Somewhere on the curve--again, whatever shape it happens to be--there will be a peak year for production. That peak year could be 2004 if some major cataclysm destroys all humanity in 2005, in which event the peak would be defined not by geology, but by catastrophe.
Dude, you reminded me of my calculus day!
Actually Rolle's theorem from elementary functional analysis predicts a peak lol
Lets see if I remember it correctly
:[a,b]->R function differentiable in the closed interval [a,b]
[b], then there is a c point where the first derivative of the function is equal to zero
But if a function is differentiable, and has a derivative equal to zero, then that point is an extremum (maximum or minimum)
So think of f as the production to date, its first derivative is the rate of production (i.e. how much they are pumping from the ground per unit time e.g. day). So what does that mean? That there is a point where the production will be maximum. Before that point, the production rate will de increasing, after that it will be decreasing till it goes to zero.
Come to think of it, it is not even college math, probably senior high math.
Not even an economist can beat both geology and math
"Nuclear power has long been to the Left what embryonic-stem-cell research is to the Right--irredeemably wrong and a signifier of moral weakness."Esquire Magazine,12/05
The genetic code is commaless and so are my posts.