The proof is straightforward.
Take the rate of growth over the last three months. Use your eyeball to extrapolate forward six months.
$6,800 pops out as the answer. Q.E.D.
I sense your skepticism.
Let's be more conservative and use a more cautious view of the rate of growth over the last six months, to extrapolate forward six months.
The new conclusion might be that Bitcoin is going to drop to $1,800 by the start of 2018. A big loss if you bought in anywhere above $2,800. But more than a double if you bought in early 2017 at $800 or below.
And the final conclusion that you should walk away from this short read with is:
Extrapolation is very dangerous.
Extrapolation has less value in predicting the future Bitcoin price than gazing into a crystal ball.
But your neural circuits have been trained over 1000's of generations to look for simple patterns. You are here today, because somewhere in your background one of your very distant ancestors was good enough at detecting simple patterns to avoid being eaten.
That makes it almost impossible for you to look at the recent six month chart of Bitcoin and avoid jumping to the simplest possible conclusion. "..... this trend has to keep going."
Bad news. The simple pattern analysis machinery that is hard-wired into your circuitry could be leading you astray.
So what will the price of Bitcoin be in January 2018?
I know I don't know.
You're on your own on this one.
Bitcoin chart from coinbase.com and picture from business-analytics-info.fr