exponential

Etymology

The OED takes the mathematical word partly as borrowed from New Latin exponentialis, first recorded in 1697 in a correspondence between B. Nieuwentyt and Johann Bernoulli printed in the “Acta Eruditorum”, formed from exponens (“exponent”) and the suffix -ālis, and partly as formed from English exponent + -ial.^[2] Etymonline, Merriam-Webster and Dictionary.com derive it from exponent alone,^[3][4][5] and the Shorter Oxford and the Oxford Dictionary of English from French exponentiel,^[6][7] which the OED finds in Bernoulli in 1704 in the phrase courbe exponentielle.^[2] Exponent is from the present participle of Latin expōnō (“to put forth”),^[3][7] the source of expound.^[3][7]

Earliest recorded meaning

Of an equation or quantity in mathematics, involving a variable in an exponent: 1701, in G. Cheyne's New Theory of Acute and Slow Continu'd Fevers.^[2] Etymonline and Merriam-Webster date the word to 1704,^[3][4] and Dictionary.com to 1695–1705.^[5]

Semantic evolution

The word was first a mathematician's term;^[2][6] Johnson (1755) explained exponential curves only, quoting Harris.^[8] The noun, an exponential expression or function, is recorded from 1704, in C. Hayes's Treatise of Fluxions.^[2][3] A rare sense "expository", formed from exponent, appears in Bailey's dictionary in 1730.^[2] Merriam-Webster notes the use of the adjective for growth in which one factor depends on another, as in a quotation from F. H. Hankins that culture grows in an exponential manner.^[4] From 1955, in the Washington Post, it was used more loosely of any increase that becomes faster and faster,^[2] and Collins labels the sense "very rapid" informal.^[9]

Timeline

• 1701 – in mathematics, involving a variable as (part of) an exponent.^[2] Etymonline and Merriam-Webster date the adjective to 1704.^[3][4]
• 1704 – noun, an exponential expression or quantity.^[2]
• 1730 – expository (rare).^[2]
• 1755 – Johnson's dictionary explains exponential curves.^[8]
• early 20th century – the adverb exponentially.^[6]
• 1955 – of an increase, becoming more and more rapid.^[2]

Meanings

Adjective

1. (mathematics) Of, involving or expressed by an exponent, especially one that is a variable: an exponential equation.^[9][4][2]
2. (mathematics) Raised to a power of e, the base of natural logarithms.^[9]
3. Of growth or change: increasing ever faster, or (informal) very rapid: The startup saw exponential growth in its first year.^[9][2][6]

Noun

1. (mathematics) An exponential function or quantity.^[9][2][6]

Word family

• exponentially
• nonexponential
• exponentiation
• exponential function

Related words

• exponent
• expound
• exponentiate

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l m n Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d e f Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b c d e Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
5. ^ a b Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
6. ^ a b c d e Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
7. ^ a b c Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
8. ^ a b Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
9. ^ a b c d e Collins English Dictionary (2023), Glasgow: HarperCollins