What is a suitable exponential to model a currency or cryptocurrency price increase? I would like to model a supply and demand cryptocurrency market, not necessarily for Bitcoin, but for any coin.

My difficulty is that I don't know what exponential factor might be realistic to do so.

For example, I was thinking to pick the exponential factor of e to the power of -10 increase per coin, this happens in case you exchange fiat money for crypto.  Same exponential factor applicable for decrease, in case that the reverse transaction is performed.

I searched online, and I can't seem to find a value for this factor, or additionally if it is static or dynamic.

For example, with the above data, if the starting value of a coin is \$300 and someone invests \$300,000 to buy 1,000 coins, the value per coin goes to \$300.0457.

But if someones invests \$3,000,000 the value goes to \$345.7, I am wondering if it is realistic given that the total coin supply is 8 Million for example?

Can someone help and reason about the choices?
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.