There is usually a lot of speculation that the bitcoin price is exponential. While there are some instances of exponential price rise when there is a self fulfilling feedback loop of excitement over a price rise which brought us the $32, $266 and $1240 prices. If we step back and look over the long term you can see a linear price rise.
I split it in two to show before and after the price halving (and to go from MtGox to BitStamp).
This would indicate that the true price should be around $310 or so right now which would explain the long downtrend.
But there are a few positives from a linear price rise. It is less volatile, it makes sense for a currency and it continues to trend up.
There is also a slight upward rise in the rate of price increase at the halving, which would indicate that in 2016 the rate will tick up a little more at the next halving.
The current price is where the linear price will be in December. If we go down a bit before then, it will probably follow close to the trend.
While an exponential rise is exciting and great if you get out at the top, a linear price rise is good in the long term.
The formula would be close to this:
P = 13.5t + 12
where t = months since November 2012
Before the halving the rate was closer to:
P = .5t + 1
t being months from February 2010
With the formula after the next halving:
P = 20.25t + 660
t being months from November 2016
You have described an exponential function..
