You’re not wrong, but colloquially it’s common for people to use “exponentially” to mean “a lot”. Just like it’s common for people to use “massive” to mean “big” (i.e. large spatial volume).

It was just an idiom as this isn't a technical discussion. I think most readers could get the idea.

Exponentially is often used to mean "10 times more". So if one date point is 10 times higher than a second data point, than the wording would hold colloquially.

Are you confusing with 'an order of magnitude'? Exponential is a rate of change, so you simply can't determine it on two data points. Order of magnitude is the relative change itself, so you can determine between two data points.

You are literally correct, and literally could not be more wrong (and I'm deliberately using both the correct and colloquial - but depressingly also dictionary defined - definition of the word 'literally' there).

Language evolves, and not always for the best.

No, but I agree that OOM is the better word choice. That's the great thing about the English language - whatever it means today, it won't tomorrow!

Also, to address the definition of "exponentially", I refer you to the second definition here [0]:

  -- "any positive constant raised to a power."

[0] - https://www.dictionary.com/browse/exponentially

That's not what that definition means in this content.

Think about it - you can express any change from A to B as a positive constant raised to a power. So if that's what you think it means then you're saying any change from A to B is rising 'exponentially'.

Well......Actually....

If I have 5 accidents and you have 25 accidents you've had exponentially more. You don't need 3 data points, x^2 is an exponent.