What is a suitable exponential to model a currency or cryptocurrency price increase?
If I understand correctly you are asking for a model of the price of bitcoin based on the number of transactions.

This is impossible for a number of reasons.
1) Theres not necessarily a relationship between those two variables

2) Even if there is a relationship between the two variables then there may be other variables which have an equal or stronger effect (very likely) making the variable a bad predictor.

3) If there is a relationship, and that relationship is not causal then knowing the relationship would cause it to cease to exist as people begin to trade on arbitrage with that model which would cause it to stop being effective.

4) If I could model the price of bitcoin I certainly wouldn't be telling you, instead I'd be living it up on some private island.

The question makes no sense and is by far too complicated of a question. This is the type of topic that requires a research paper and will not necessarily provide results.

This is why you are getting downvoted. Because there is no logical answer to what you are asking.