In a manner that increases at an accelerating rate, where the rate of change becomes proportional to the current value. Mathematically relating to exponential functions.
From Latin 'exponere' meaning 'to set forth, explain' plus '-ential' and '-ly' suffixes. The mathematical sense developed in the 17th century with the rise of advanced calculus and mathematical notation.
This word perfectly captures one of nature's most powerful patterns - from population growth to viral spread to compound interest. When something grows exponentially, each step makes the next step bigger, creating the dramatic curves that shape our world.
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