The price is only determined by who is buying and selling right now. Trading at $45 merely implies a nonzero number of shareholders value Twitter at $45.
(This is also why we can use this price to indirectly learn something about how the market views the likelihood of Elon buying Twitter: if it were a "sure thing", the price of Twitter stock would be trading close to $55, as you'd be able to make a fast profit.)
The way I see it, people (and other entities!) don't think Twitter is worth X, they think there is a distribution of worth.
This means there is risk in their bet, so if I thought Twitter was worth (on average) 100USD, that wouldn't mean I would sink my life savings into it but would put in some, based on the risk and also what else I need capital for.
Also, how much one thinks Twitter is worth probably also depends on your time horizon: like the old adagium that the market can stay stupid for longer than you can stay solvent, e.g. when shorting a scam.