Hi, I just made a graph of the data from bitcoincharts.com for MtGox USD, taking all 6-hourly data since their records begin. Bitcoin seems to go through phases of exponential growth, which probably means that it spreads virally through a new class of user before saturating its presence in that group. I had a pet theory a while ago that each new phase of expansion of bitcoin would always be slower than the last, but this latest increase to $65 is actualy faster than the previous two. However it is significantly slower than the June 2011 bubble, which saw the price double almost 3 times as fast as it is doubling today.
http://imgur.com/L3raefvFor those that don't know, exponential expansion indicates that, on average, every entity participating in some network is bringing in another entity in some fixed time. It could be rabbits breeding, or cells dividing in a foetus. From 1 cell or rabbit, you get two. From 2, you get 4. From 4, 8. And so on. Each doubling occurs in the same time.
Right now, bitcoin price is doubling every 33 days or so. If this were to keep up (which it won't, I'm certain) until year end, bitcoins would be worth about $16k each, and market cap would be about $200 billion. However, each of the previous exponential expansions lasted typically about one or two months each. Which would suggesting we're near the end of this one, assuming no externalities to disrupt the trend (like global banking collapse).
A singluarity (mathematically) means the price would start to diverge; i.e. much faster than exponential. There is no indication of that in the graph.