9th Jan to 18th Mar: I concur, that is the inherent BTC increase rate.
Your blue line is correct IMO.
If the USD doesn't crash one BTC will have a value of ca 1000 USD in a couple/few years. The blue line will even give the predicted month. Spike(s) could see an ATH over 1000 USD months in advance of the BTC value actually being so.
Fine graph.
I don't get it, how do you get to "1000 USD in a couple/few years" from "blue line is correct IMO"?
ManBearPig says it represents a daily growth of 1.8%. Let's be cautious and start today at 120 USD. In a year from now, we would be at 80,745 USD. Kind of unreal, huh?
Welcome to the magic of compounding

Google it, it really is called that for a reason!
Try it yourself using this great little tool (or make a little Excel sheet):
http://www.miniwebtool.com/compound-growth-calculator
I don't extrapolate that far ahead on my recent graphs because it makes me look a little crazy but the figures are all there for you to see as in the case above: $13.77 is where what I believe to be the underlying trend of 2013 began.