1. Fit to the data - here you have not really explained what did you try. I take your word that for all functions that you did exp was the best fitting - but I have the feeling that your imagination about the possibilities is limited.
2. Relation to the observed mechanisms that produce the data - You don't mention any mechanism. I write that relation to time passing is better then relation to sun spots - cos(t) would also be related to time passing. A dumped oscillator function would actually have some relation to the observed mechanisms that produce the data - if we agree that people tend to predict that the price will go in the direction it goes now and that people predictions do influence the price.
3. Predicting future -
perl -e 'print 10**(-2.869800 + 0.003012 * 6000)'
1.59294213512763e+15
And that is a 1000 times more than all money supply on Earth (M0 is around 1.2e+12).
Evidently exp function cannot predict the future too far away and eventually it will have to be replaced by some S curve or maybe a dumped oscillator or something else. Maybe even something with a trigonometric function in it (the simplest oscillators)?
Yes, it seems that you have understanding on the subject, and also are probably doing quite well. It is difficult to try to distill the essence of quite long studies to an easily chewable form for people who do not understand the fundamentals of Bitcoin, nor of the model, while at the same time swimming in a sea of trolls.
I have no intention to waste my precious time more than is needed to rigorously prove to a nonexistent audience, why and how the model needs to be amended to take into accout the edge cases when it has turned the entire Earth into Bitcoins, nor what is my estimation of the probability that the model holds another year, nor what are the bounds for the model to "hold", nor many other things.
These are all important matters, but the capability of my audience to understand them and make informed decisions based on them any more than based on the "plain post" alone is just not there. If someone wants to buy bitcoin, my posting can help. If he does not want, he either cannot understand any deeper reasoning, or maybe he can, but his mind is made up nevertheless.