Starting from today, I will offer a regularly update of the bitcoin long-term exponential trend. Please consider to donate if you like this service

Method:

Data source: bitcoincharts.com daily volume weighted average price (VWAP)

Reference exchange:

17 Jul 2010 to 18 Jun 2013: MtGox

19 Jun 2013 to now: Bitstamp

Dates omitted:

20 Jun 2011 to 25 Jun 2011 (MtGox closed)

6 Jan 2015 to 8 Jan 2015 (Bitstamp closed)

Regression model:

y = ax + b,

where y = natural logarithm of VWAP; x = days since MtGox inception, 17 Jul 2010 = 0; a = slope; b = intercept

Glossary:

Rsq: R-square value of the regression model

Today's expected price: The expected price of today based on the regression model

Predicted date for today's price: The expected date for today's price based on the regression model

Days ahead (behind): The difference between today and the predicted date for today's price. A positive value indicates we are currently above the regression and vice versa

Daily price rank: The rank of today's VWAP among all historical VWAP. 1 means the all-time-high VWAP

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Date: 16 Feb 2014

VWAP = 625.45

x = 1310

a = 0.006037

b = -1.82098

Rsq = 0.871816

Today's expected price = 440.0484

Predicted date for today's price = 15 Apr 2014

Days ahead = 58

Daily price rank = 84

Predicted date for ATH ($1126) = 26 Jul 2014

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tl;dr:

ASSUMING the bitcoin price is growing with an exponential trend in long-term:

We expect bitcoin price to grow by about (1 - e^a) = (1 - e^0.006037) = 0.6055% per day

87.1816% (Rsq) of the variation in bitcoin price could be explained solely by time (which is very high)

The long-term "fair" price of today is only 440.0484. We are outpacing the long-term trend.

We expect to see today's price (625.45) on 15 Apr 2014, which is 58 days later

We expect to see ATH (1126) on 26 Jul 2014

Today's price is the 84th highest in the history of bitcoin

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y-axis is ln(price)

Blue line is the daily VWAP

Red line is the expected price of the day. For each day, a regression is fitted with all data of and before that day, so it is not a straight line.

Green line is the current regression line

Btc is getting popular in time not just here in the country but also outside because as much as I observe many people have heard many good things about it and began buying and saving coins.