Indeed. It's been a while since I've had to so much as think about big O notation and I forgot that quirk. To most folks "exponential" means n^2 or greater
When family talks to me about covid spreading exponentially I am pretty sure they mean n times n, or n^2
Yes we all know the technical definitions with respect to software and algorithmic complexity. But the lack of sympathy/empathy on display with how a common definition of a word can be misconstrued by someone without an academic background in tech is kind of surprising (ok well maybe not so surprising but c'mon folks, we are all human)
So 2^n would be exponential. However, n^2 is instead quadratic.
Quadratic time complexity is better than exponential.
Here is a useful comparison of the rate of growth for various time complexities[0]
[0] https://stackoverflow.com/a/34517541/3574076