It is going to evolve in some kind of random way but the truth is that no one really knows how, so they try some models. The simplest model which is reasonable is called geometric or exponential Brownian motion. Let's try to describe it. The main idea here is that the market is made up of a lot of very little investors, so price movements that we observe are sums of a great number of random small movements. But also the stock price grows at some rate .
All prices also have to be relative to the total price.
If you take the limit of the equation you get called a stochastic differential equation . So the equation is really strange and it took until the 1950's before people even started to make sense of it. In fact these functions are so strange that the ordinary rules of calculus, like the chain rule and the product rule and integration by parts are just not true. But there are analogues. In normal calculus the last term wouldn't be there.