There's this theory that oil production will go up ... then it will go down.
When things like that happen, mathtypes (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 
