Peak Oil

There's this theory that oil production will go up ... then it will go down.
When things like that happen, math-types (almost) immediately assume a Normal Distribution function will fit the data:

If that were the case, then the logarithm would satisfy:
 log(f) = A - K (x - m)2 ... for particular values of the parameters A, K and m

That's a parabolic curve ... so we'll try fitting such a curve to the logarithm of the Oil Production data.

We get this (where the "best" fit is the one that minimizes the Root Mean Square error between the data and the curve):

>What's them grey curves?
The parameters have been adjusted up or down by 1% ... to see how sensitive the "best fit" is to that kind of change.
>So ... is that a good fit?
Wait and see.
 >Is that the "best" fit? You can play with the spreadsheet below and use your own imagination as to what's "best". I should point out that lots of people do this sort of thing: Using Average Error as definition of "best fit"

 Year Production 1965 31,806 1966 34,571 1967 37,121 1968 40,438 1969 43,635 1970 48,064 1971 50,846 1972 53,668 1973 58,465 1974 58,618 1975 55,826 1976 60,412 1977 62,714 1978 63,332 1979 66,050 1980 62,948 1981 59,535 1982 57,298 1983 56,599 1984 57,686 1985 57,472 1986 60,463 1987 60,784 1988 63,154 1989 64,042 1990 65,460 1991 65,268 1992 65,774 1993 66,028 1994 67,104 1995 68,102 1996 69,897 1997 72,185 1998 73,538 1999 72,325 2000 74,861 2001 74,794 2002 74,431 2003 76,990 2004 80,256 2005 81,089 2006 81,497 2007 81,443 2008 81,820

>Ya know, that red curve don't look much like a Bell Curve.