I'm not the OP you're responding to, but to be fair, in a sentence about big-O perf characteristics, which includes the word "algorithms", using "exponentially" in a colloquial non-technical sense is an absolutely terrible word choice.
I disagree. Misuse of the word "exponential" is a major pet peeve of mine. It's a particular case of the much more common "use mathematically precise phrasing to sound careful/precise" that you often find in less than honest writing.
Here they are actually using it to refer to growth functions (which is rare for this error) and being honest (which is also rare IMO) but it's still wrong. They should have written about quadratic or quadratic vs linear.
Regardless sloppy language leads to sloppy thought.