Need help understanding how the pricing of stocks works

Okay, so I know that the price of a stock rises when there are more buyers than sellers, and this generally happens over time because the company itself is growing over time. But my question, that I can't find a clear answer to, is why does the growth of a company generally correlate to it's stock price growing over time? I could understand this if it meant buyers had a direct claim to the profits of a company since that would connect you to more cash, but you really don't. Of course there are

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