It can't go on forever, and the time to double certainly can't keep getting shorter at the rate it has been.

Beyond that it's impossible to predict what will happen. The increase could slow down to merely being exponential, consistent with a stable adoption curve. There could be another 2011 style crash followed by a year to recover. We could see more people pour into Bitcoin until we pass through the Singularity and wake up 3 months from now to a world where nobody uses dollars or euros any more.

Or it could crash to worthlessness.