However that doesn't mean bitcoins are in a bubble, for that the true value would have to be lower than what it is. And I don't know how to even roughly estimate bitcoin's true value. That is, what the price will turn out to be in the long run, what the supply and demand will be. That depends on how big the bitcoin economy will grow, and the hype, while irrational, might actually bring enough people to it to make it work. Or it might just die as people get disappointed or move onto the next thing.
In this case, Bitcoin price growth made it more popular, which caused more people to start investing in Bitcoin, which further increased its price. The exponential shape of Bitcoin's price curve is entirely normal.
The real question is, does Bitcoin's current price match its "true" value? I personally believe the answer is "no", but that's like, my opinion, man.
I guess my issue is what you mean by that. When people see Bitcoin's price shoot through the ceiling, I totally agree that it attracts them to speculating on the currency, further exacerbating the increase in price, causing an exponential shape.
It is not clear that its price increase would attract people to using Bitcoin as a currency and not speculation though. I consistently hear about the importance of a currency having a relatively stable value so I wonder if large, rapid price changes actually discourage using Bitcoin as an actual currency while encouraging its use for speculation (or at least not encouraging its use as a currency).
It would not make sense for anything that has independent utilitarian value to have anything but a growth rate that is correlated with that value. It would seem that exponential deviations from such a growth rate could only be due to speculative mania. If people are only or mostly buying Bitcoin because its price has increased, hoping for a further price increase, then there is only so high the price can go before collapsing.
Rereading your comment, maybe we're actually saying the same thing here.
I believe that, like you mentioned, it depends on Bitcoin's utilitarian value as a currency. If it turns out Bitcoin is more useful than, say, Paypal for facilitating actual transactions (as opposed to being a pure investment vehicle like it's being used now), then its price should encounter steady growth. If not, then things will get interesting.
And more on it's market irregularities (take for example the inability to withdraw USD via the SWIFT banking system without a 6 month delay from MtGOX)
It makes "price discovery" in the sense of a true currency valuation very hard to estimate, and the illiquidity makes the instrument very prone to HUGE run-ups and sell-offs. I actively trade it, and believe that a price target of over $1000 is a strong technical possibility. Though what it "resets" to after this run-up is anyone's guess.