Please Explain why we take the product of two variables in a rate model (or any model)?

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I'm trying to understand this equation: v = k[A][B] where v is the rate of a chemical reaction, k is the rate constant, and A and B are reactant concentrations. I think this equation relates reaction rate to the reactant concentrations by a proportionality constant, k. I just don't understand why we multiply everything on the right side- what does that mean physically? More generally, why do we multiply variables together in a model and would we always need a proportionality constant to relate the right side with the left side? This equation comes from general chemistry for modeling reaction rates.