Hmm - do you say that the line you are watching is not 'USD/BTC = exp(-2.869800 + 0.003012 * D), D being the number of days' anymore? Have you changed the coefficients or have you changed it altogether so some other function?
It is always, every day, the line (or other construct) that gives the highest R^2 fit with the USD/BTC price data between 2009-1-3 and present_day. For all the time it has been an exponential function, which is linear when plotted in logarithmic space as I do.
Your comment about only one best fitting trendline only makes sense if you constrain your search space - for example by choosing only exponential functions.
A side note - if you for example allow for trendlines to be polynomials of unrestricted degree - then you'd be able to fit the trendline to the price chart exactly (with no divergencies at all).
1. Not really. Others just don't come close. 2. That's quite theoretical, since I cannot convince myself that a model with more than 2nd degree term is anything but noise with no predictive power, and Excel allows construction to 6th degree, with no improvement in R^2.
What IS important is if the growth trend is slowing or not. I currently hold the opinion that the trend is pretty much intact and price is about to increase 10x in a year. AnonyMint thinks it has slowed.
How about trigonometric functions? Have you tried them? Or polynomials with trigonometric functions? I am sure Excel have many many functions and you can combine them in many many ways - I am sure you have not tried them all. So my question is how do you chose your functions - why are you sure that exp is good and cos is not?