There are assumptions in your thinking that probably are not valid. You are observing exponential growth in the short-run and assuming that the valid model is exponential. There is plenty of theoretical reasons to believe that this is not true.
To give you a real counter-example where your observation would have failed you, you should consider the tulip bulb mania. It began rationally enough. A virus infected tulips in Holland and this caused some tulips to become multicolored rather than monochrome. The multicolored tulips were in short supply because people felt they were pretty. The price of a tulip bulb in Holland at the time would have been less than a current dollar.
This led people to buy out the bulbs because supply is perfectly inelastic in the short run. So people put in advance orders for next year's crop. They received receipts. This state of affairs went on for a few years and then people began trading the receipts. A futures market had developed. Prices grew at an exponential rate because speculators entered into the market. After all, nobody had ever lost money in the tulip bulb market.
By the end of the speculation single bulbs were trading at what would be over a hundred thousand dollars per bulb. Then it stopped. You see a tulip bulb has pretty fixed real world utility. It looks nice, but you can grow more. The same thing is happening in cryptocurrencies. While the approximate number of bitcoins, for example, is nearly perfectly inelastic in the short-run, you can always create a new cryptocurrency. There are now hundreds of them. If a central bank comes out with its own cryptocurrency, it will probably collapse all of the private ones as it will be backed by the state. The state will also have an interest in profit maximizing by exhausting the demand for them. If you are wondering about what happened to the tulip bulb market, well go to a greenhouse and buy one.
Prices are growing exponentially for a variety of reasons. You mentioned one of them, which is well understood. Prices grow or shrink, depending on whether you are buying or selling, exponentially in volume. This is due to the fact that the party making a market in them has to charge the carrying cost of the inventory and so the rate of exponential mark-up is related to the half-life of the position, hence the exponential element.
That is true in the stock market, the bond market and the art market. The carrying time of a position determines its price.
In the long run, the value of a cryptocurrency will be equal to the costs avoided. If using a cryptocurrency allows you to avoid a cost created only when using lawful currencies, then that will determine the value of the cryptocurrency. Some, like Etherium, allow you to engage in self-executing contracts. The value of the currency will be based on the savings of using a credit card to do the same thing minus the inconvenience of having to buy and set up the accounts.
Cryptocurrencies are probably worth a very small amount of money. When the speculators leave, it will be done.
For the volume you are looking at a mark-up or mark-down of exp(m(t)*n) where n is volume and m(t) is the carrying cost adjusted for the half-life of the position. If buying from the market maker you would multiply the price by this factor and if you were selling to the market maker you would divide by this amount.
This number is probably unstable at the moment and won't become stable until the market finally falls apart. It won't be in the collapse that you will get a stable m(t), but rather probably a year later. People make a market in tulip bulbs buying them from growers and selling them to retailers. Their mark-up and mark-down do not look at all like the mark-ups or mark-downs during the mania. I like tulips, but probably won't pay a hundred thousand dollars to buy a bulb.
One final note, money is a dominated asset. It is always the least valuable asset in the system. To understand why, open up your wallet and take out a dollar bill. Is it earning you any interest? Is it causing a car to be produced? Can you eat it? Would you prefer to use it for toilet paper or Charmin?
US money holds its value only because the government requires people to pay their taxes with it. Private money existed before the Civil War and the government ran the competition out. Since you have to pay taxes with it, it would be helpful if it was useful for other purposes. Since everyone has to pay taxes, everyone needs it, although only just enough of it. Most people do not carry all their money wealth with them. They put it in banks. Banks are the sink for all these dominated assets because they sell them through loans to people who need them the most and buy them through deposits to those who have an excess amount.
Since cryptocurrencies cannot be used to pay taxes and there are no deposit or loan relationships present, it is difficult to imagine how much value they could maintain in the long run. Only a handful of private currencies exist in the United States, such as BerkShares. They will hold as much value as possible when people can go to a bank and borrow them to pay for a car. If that doesn't happen, then they will be even more dominated than cash.
