Now, we can not proof that bitcoin economy is growing exponetially in its number of members attracted to. Some actual data leads to suppose, there is no growing, last 2 months.
You may analize averaged BTC volume on top BTC exchanges, such as MtGox, etc:
http://bitcoincharts.com/charts/See,
v (1) ~ const, t <- [Apr 1 2011, Jun 1 2011]
if m(t) ~ exp (t) then v_p_m (t) ~ const/exp(t) ~ exp (-t),
whrere
- v (t) - total BTC volume in work, of all BTC exchanges, per day, averaged by two-week window
- m (t) - total number of people (members) who playing on all BTC exchanges, per day
- v_p_m (t) - average BTC volume per member per day, the member plays with on all BTC exchanges
So, v_p_m (t) ~ exp (-t), in BTC, or v_p_m_$ (t) ~ exp (-t) * ($/BTC) (t), in $,
where
- $/BTC is BTC average rate, currently ~ $9.5/1BTC
For v_p_m_$ (t) to be slightly growing, or at least const (indicates whether BTC economics is really growing),
we need ($/BTC) (t) ~ exp (+t).
Inflation? No. Deflation. Because we remember, v_p_m (t) ~ exp (-t).
Exchange members & all other bitcoin society members will keep BTC rather than sell/buy for BTC. Because keeping is simply EASY and is profitable *exponentially*, due to ($/BTC) (t) ~ exp (+t).
So, while ($/BTC) (t) ~ exp (+t), bitcoin ecomonics IS FROZEN,
furthermore, if we will see ($/BTC) (t) ~ const, in near future, it leads to
v_p_m_$ (t) ~ exp (-t). if ($/BTC) (t) ~ exp (-t), then v_p_m_$ (t) ~ exp (-2*t) => bitcoin ecomonics WILL COLLAPSE.
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So, THE THEOREM:
If we assume number of BTC exchange's players (members) is growing ~ exp (+t), and if we observe average BTC volume per day ~ const, bitcoin ecomonics WILL FREEZE OR COLLAPSE.
Now, average BTC volume per day on all exchanges ~ const for TWO MONTHS.
BUT APPARENTLY, averaged ($/BTC) (t) ~ exp (+t).
And also has strong correlation with mining network's difficulty.. Why?
