What Is Exponential Growth?

This article was updated and republished on March 25, 2020. Transcript text may not match the podcast audio.

A while back, I ran across a tweet from B.J. Novak (aka, Ryan from TV's The Office) stating: "The misuse of the word 'exponentially' has increased dramatically.”

If you know what the word “exponentially” actually means, then you probably agree with Mr. Novak’s observation that there has been a dramatic (although not truly exponential) increase in the misuse of this word. Nowadays, people utter "exponentially” as another way of saying “rapidly” (or perhaps “really rapidly”). But mathematically, that simplifies the definition a little too much.

So, what does exponential actually mean, math-wise? What are some actual, non-hyperbolized examples of real word exponential growth? And how can you save yourself from making this mathematical faux pas? (Or is it even a faux pas at all?)

An exponential increase in “exponentially”?

If something is growing exponentially, it's growing rapidly … very rapidly. But it’s not just that—it’s growing rapidly in a precise and predictable way. At least according to the proper mathematical definition of the word (more on exactly what that is in a minute).

If something is growing exponentially … it’s growing rapidly in a precise and predictable way.

Of course, these days people are a lot more relaxed with the word. Take, for example, Twitter user and NBC New York reporter @Checkey4NY’s recent tweet stating that “Crowds on 5th Ave have literally grown exponentially in just a few minutes.” I particularly like this tweet since it includes both the newfangled version of “exponentially” as well as the often funny word “literally” (because it’s so frequently used to mean figuratively). In other news, sportscaster @SportsBoyTony noted in his recent tweet that “[Collinsworth] gives you exponentially more than Simms.” And finally, in a totally different vein, Twitter user @iMuggle recently tweeted “I just remembered we are having sushi for dinner. [The] day just got exponentially better."

If you know the actual mathematical meaning of the word “exponentially,” you’ll...

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