Definition:Exponential Function/Linguistic Note
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Linguistic Note on Exponential Function
The word exponential derives ultimately from the (now archaic) verb to expone, which means to set forth, in the sense of to expound, or explain.
This itself comes from the Latin expono, meaning I expose, or I exhibit.
The word exponent (from which exponential is formed) therefore means a person (or statement) that explains something.