"Doubles every year" is just a simple way of summarizing geometric growth to the layman. I'm sure info generation doubles every t, but the chance of t being very close to one year is quite low.
Other, less dramatic kinds of growth can appear exponential in its early stages. I'm always amazed at Internet growth data that are only fit to an exponential -- "at this rate, our startup is going to take over the universe in five years!"
Has everyone forgotten about logistic growth? There is probably a ceiling to most growth, wouldn't it make more sense to ask where it lies? http://en.wikipedia.org/wiki/Logistic_function
I agree with you in general, but you picked a funny example to make this case - generation of information doesn't seem like something which will level off after a while.
Edit: if you think of the logistic function as modeling the rate we create information, this is one possible "story": initially there's slow growth due to technology. Then the technology picks up, and there's the exponential phase we're seeing right now. That settles into a nice linear trend as the tech matures. Finally, we hit either natural (e.g., satiation) or technological limitations and that slows the rate of growth. At the very limit, we're still creating information, but at a constant rate. The rate of growth might be near 0, but the rate of production is still bloody high.
