"It is doubling now every two years. Doubling every two years means multiplying by 1,000 in 20 years. At that rate we'll meet 100 percent of our energy needs in 20 years."
Simple. Next problem?
This is a case where I have a hard time believing an autoregressive model. At some point, if folks do not come up with a scalable, efficient solar energy solution, the use of solar power is going to stop doubling every two years. If they do come up with such a solution, then the use of solar power should start doubling faster. I think it would be very lucky if we were to see an average of doubling every two years for twenty years.
My personal views on the alternative energy technologies that will yield the best returns on investment for implementation (not counting research, which needs to be done up front):
Starting now: conservation measures; upgrades of the power grid to make it more efficient and more intelligent (Cue Lynne Kiesling); new coal and nuclear power plants.
Starting in five years: cars that run on batteries, re-charged from the grid (often called plug-in hybrids). But we'd better have construction underway by then of those new coal and nuclear power plants.
Starting in fifteen years: fuels produced by bio-engineered organisms.
Starting in fifteen to twenty-five years: large scale solar power.
My guess is that about a decade from now "wet" nanotechnology (bio-engineered organisms) will have taken a big lead over "dry" nanotechnology, which is what most of the solar folks are thinking about. In fact, my expectation would be that the scalable, efficient solar solution will involve bio-engineered thingies.
Never becoming economical: hydrogen delivered in a way that is analogous to gasoline (we might see hydrogen used as part of the solution for re-chargeable batteries, but I doubt it); conventional biofuels (instead, biofuels will require yet-to-be engineered organisms); wind; coal-with-carbon-sequestration (by the time we figure out how to make sequestration practical, we'll have figured out that CO2 is not a big factor in climate)
This is just intuition. I am not a scientist. The only people less qualified than I am in this area are the politicians who will be directing our energy policy.