“The number A is exponentially greater than the number B!” What does this mean? Nearly nothing. If it has a meaning, it’s that there’s some number x such that B^x = A. But that’s true of any two numbers, as long as they’re both greater than 1 and A > B. Please don’t use that expression in your writing.

You could also say that A is “linearly greater” or “quadratically greater” than B. They’re just as true and just as meaningless. “Exponentially greater” sounds more impressive because exponential curves rise really fast. In the early days of the coronavirus pandemic, the number of cases followed something close to an exponential curve. But a single data point doesn’t establish a curve.
(more…)