It used to bother me too, and some usage still bothers the hell out of me, but there’s a way "exponentially large" works fine.
An exponential change is a change on a log scale. Instead of current+d it’s exp[current+d]. So exponential change makes sense. “Exponentially higher” means on a log scale it’s higher enough to be worth commenting on. It’s mathematically correctly synonymous with an order(s) of magnitude change.
Of course, that gets you into the debate over what exponent or log base to use. Is 2x an order of magnitude increase? 1.1x? 10x? It’s all fuzzy.
And then there are people who just use it as “hella” and that still drives me nuts. “It increased by 10% but that matters so much to me that 10% is exponentially larger!” That kind of usage seems to be catching on too as “exponentially” further enters the lexicon of people who don’t remember what an exponent is. I’ll fight that one forever.
An exponential change is a change on a log scale. Instead of current+d it’s exp[current+d]. So exponential change makes sense. “Exponentially higher” means on a log scale it’s higher enough to be worth commenting on. It’s mathematically correctly synonymous with an order(s) of magnitude change.
Of course, that gets you into the debate over what exponent or log base to use. Is 2x an order of magnitude increase? 1.1x? 10x? It’s all fuzzy.
And then there are people who just use it as “hella” and that still drives me nuts. “It increased by 10% but that matters so much to me that 10% is exponentially larger!” That kind of usage seems to be catching on too as “exponentially” further enters the lexicon of people who don’t remember what an exponent is. I’ll fight that one forever.