This should not be possible.

An exponential component is what you should mean, and that is very likely in a situation where new people continue to learn about Bitcoin and subsequently start using it. Of course, exponential growth will not continue after Bitcoin becomes macroscopic, which could be within months if things go on the way they are going now. However, you have no reason to expect price or the amount of Bitcoins traded to grow exponentially because of that. Currently, we have speculators -- later, we want traders! The transition will change how reach and price are linked.

Your reasoning assumes Bitcoin behaves like a Ponzi scheme. This need not be in the long run, and the profit margins allow speculators to wait patiently for quite a while. You must take into account that many speculators estimate the potential target price and success probability before buying. Those two multiplied are not growing exponentially just because the number of users is.