exponential

What it means

1. mathematicsExpressed in terms of an exponent (power of a base), the base often being 10 or e.

   In base-10 exponential form, 1,000,000 is written as 10⁶.

   1 more example

   If not otherwise specified, "the" exponential function is normally understood to mean eˣ.

2. mathematicsCharacterised by a rate of change that is proportional to the value of the varying quantity, or, equivalently, by a doubling or halving over successive fixed intervals of time or other parameter, described as exponential growth or exponential decay.

   There were two deaths on Monday, four on Tuesday, and eight on Wednesday. The rate of increase seems exponential.

   1 more example

   ... Students apply the definition of slope to various representations of growth functions to discover differences between exponential and constant rate of growth.

   2013, Yvelyne Germain-McCarthy, Bringing the NCTM Standards to Life: Best Practices, High School, page 101

3. broadlyCharacterised by a very rapid rate of change, especially increase, or merely a very large amount or degree.

   Near-synonyms: extreme, huge

   4 more examples

   There's been an exponential rise in the number of crimes reported this year, compared to last year.

   If loans are not what you are looking for, then search for scholarships [...] I have been putting together scholarship letters for parents over the past decade, and there is an exponential amount of money to be had.

   2011, Michael Kiers, College Convo - Overview of College Admissions https://www.google.co.uk/books/edition/College_Convo_Overview_of_College_Admiss/MqvdAwAAQBAJ?hl=en&gbpv=1&dq=%22exponential+amount%22&pg=PA26&printsec=frontcover

   It is also about an arms control forum that has been meeting just once every five years for decision making on topics that are moving with exponential velocity [...]

   2013, Daniel M. Gerstein, National Security and Arms Control in the Age of Biotechnology https://www.google.co.uk/books/edition/National_Security_and_Arms_Control_in_th/Bf2tAAAAQBAJ?hl=en&gbpv=1&dq=%22exponential+velocity%22&pg=PR11&printsec=frontcover

   Of course, one can creatively conjure up a host of things robot-politicians can do at exponential speed and scale, from shaking hands and kissing babies to handling the fundraising “robocalls” that frustrate American voters.

   2018 July 31, Alvin Carpio, “Is it time to automate politicians?”, in The Economist

   Synonyms: extreme, huge

In a sentence

In base-10 exponential form, 1,000,000 is written as 10⁶.

Where it comes from

1. Englishexponent
2. Proto-Indo-European*h₂el-
3. Proto-Indo-European*h₂élisder.?
4. Englishexponential

From exponent + -ial.