That's what this chart is showing. The blue line is the number of bitcoins in existence as of the block number shown on the bottom axis. The number of bitcoins is exactly a function of the number of blocks, and the function is asymptotic. The years shown on the top axis are approximate, based on the target block rate of one block per 10 minutes. In reality, we're somewhat ahead of schedule because the hash rate has been increasing so aggressively.

All the difference of the world in a world where the world reserve currency inflate 40% a year and 0 the next (Money Base of the USD 2013 and 2014).
Some day, bitcoin inflation will be 4.5% year (from july 2016), 2.25% year (from 2020), 1.125% year (from 2024), etc.

Today, 1-1.5 M$/day are converted in bitcoins (both cash or goods and services) to keep up with this exchange rate.
With half of the bitcoins mined, the same amount of fiat would move the exchange rate to 640$; a quart of bitcoin mined would push the price to 1280$.
But, with the supply of bitcoins increasing less than the supply of USD, this exchange rate would raise a lot higher and faster too.

Because the price on each exchange is decided by the last trade.

yes, a comparative plot with bitcoin money supply inflation versus the same of USD, EUR, YEN, CHF GBP (M0 figures?) might be enlightening. Particularly with the recent QE antics.

If anyone would like to point me to sources (or share them if not public) for data about the Money Base and M1 of €, Yen, Yuan, UK Pound I would appreciate and compile the same chart for them.

Really nice chart OP appreciate it!!!

That chart does not even work because you would have to implement the bitcoin decline etc.

Very clearly presented chart 

..somewhere from 18 months to 5 years, depending on the behaviour of the mob getting spooked into thinking their monies are losing purchasing power (inflation expectations), so largely perception driven and manipulable by TPTB pulling levers frantically, but ultimately inevitable.

It must be clear that currency inflation do not immediately become price inflation and the increase of currency do not translate in the same increase of prices.
This because where the money flow it is not the same.
For example: if the central bank create more USD and then loan to the bank and the bank give more mortgages to the people at lower interest rates, the price of the houses will increase first. Builders will get more money and they will start spend it is some way. With higher housing prices, builders will increase the rate of building and the prices of wood, sand, concrete, etc. will increase after the prices of housing. The price of bread would not increase until later, when the investments in producing foods will reduce, the people start spending the new currency units in food, cloths, etc. If people decided to save money, you could not see any price increase (apart for the housing bubble) for a few years. Until they start spending their savings.