Since fiat currencies are not backed by anything, even gold anymore, they should all collapse eventually through hyperinflation as the temptation to devalue the currency (and associated debt obligations) through printing is just too great (see also the Cantillion Effect)
This process should be accelerated by Bitcoin as an unstoppable deflationary alternative store of value by causing speculative attacks on all fiat (I give a rough estimate of 50 years perhaps a lot sooner).
As they hyperinflate and collapse Bitcoin price in each fiat currency should approach infinity (i.e. how many Zimbabwe dollars is a bitcoin worth? Near infinite as it is no longer in circulation and only has collectible value).
Eventually all fiat currencies will have failed (including the dollar but it will probably be the last one as they will start to fail weakest first like Venezuela) and bitcoin is the only global unit of account, meaning nothing is priced in dollars or euros anymore as they no longer exist, everything is priced in bitcoin and there is no other frame of reference to price things in other than perhaps gold (but hey we're talking like 2070 at this point and who wants to pay for things with a shiny rock when we have augmented reality built into our vision or whatever cypherpunk future we are living in at the time).
As these currencies fail Bitcoins value should increase in value faster and faster asymptotically approaching infinity when priced in fiat terms until people stop using the fiat currency as it is seen as worthless (a wheelbarrow of money to buy a loaf a bread, etc.) at which point there is no objective way to measure BTC value in the failed fiat.
Once all fiat currencies have failed Bitcoin will be the single global unit of account then at that point the purchasing power of bitcoin would continue to grow but at a decreasing rate until it has absorbed all store of value function for the entire planet and settled at a "stable" final price and would then only grow or shrink in relation to global production output. This is the latter half, flattening of the S-curve after universal adoption but we have not even hit the inflection point yet so there is many orders of magnitude of growth remaining before that point.