Quadratic in this specific case, or more generally: polynomial.

It doesn't help that most people in journalism use the phrase exponential growth to describe quadratic growth.

We call that polynomial, not quadratic.

No, you're 100% correct.

O(n^[number]) = polynomial, with O(n^2) being quadratic.

O([a number]^n) = exponential.

I guess the authors aren't big on CS fundamentals?

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)