Eli5: Why are exponents so common in scientific formulas? Why is it so common that numbers in nature are multiplied by themselves?

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Eli5: Why are exponents so common in scientific formulas? Why is it so common that numbers in nature are multiplied by themselves?

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Any sort of relationship that depends on the shape or a geometry of a system or process will have exponents that represent different parts of geometry. In other words, if a relationship depends on area, you may see an x^2. If it depends on volume, you may see an x^3.

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