That's an amazingly good exponential fit for the last 20 years both India and China. Did US data fit a similar equation early on and, if so, what happened next? That could give clues as to what China would like to do next un an unconstrained world.

Speaking of the irresistible force meets the immovable object...

"RUPPERT-CORSI RADIO DEBATE CANCELLED AT LAST MINUTE
Today FTW's agent publicist Ken Levine received a call from radio station KHNC in Denver. The short message stated that Jerome Corsi would be unavailable to debate FTW Publisher Mike Ruppert tomorrow as scheduled and that Corsi's staff would call to reschedule next week."
http://www.energybulletin.net/11493.html

However,the Subcommittee on Energy and Air Quality of the US House of Representatives are going to be "Understanding the Peak Oil Theory" at 09:30 ET December 7, 2005 (today, Thurdsday) and you can watch it:
http://energycommerce.house.gov/108/Hearings/12072005hearing1733/hearing.htm

That's just what I thought when I saw those graphs. See the PFD linked to in my post above for exactly the data about the US you're looking for!
Many thanks Chris, looks like it stays exponential until it gets hit by external events - in the USA case the oil shocks of 1973 to 1980. USA consumption looks to have resumed a linear uptrend from 1980 having dropped about 20%, but that's a guess based on glancing at that graph.
That US House of Representatives hearing sounds interesting.  Will the audio be online?  If not can someone record it for us?
Video and audio online, checkout the link. I would expect CSPAN to have video recordings available online for some time (months) after the event as well.

The EIA, bless their cotton socks, also think that US demand is set on a linear uptrend:
http://www.eia.doe.gov/oiaf/images/fig3_wouttitle.jpg

...but sometimes I think that straight lines and averages are the only maths the EIA use in their forecasts ;-)