Eli5: Why are exponents so common in scientific formulas? Why is it so common that numbers in nature are multiplied by themselves?
In: Mathematics
While the other comments give good explanations of some important use cases I feel like it Taylor series also deserves a mention. Taylor expansion is a powerfull technique to describe any function as a polynomial. Depending on the process you are modelling and the accuracy you need the exponents may get large. That is not to say that the underlying physics are exacly polynomial, but for our purpose it may as well be.
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