"Exponentially" isn't all that bad; what people actually mean when they say it is usually "superlinearly", but there's no practical difference between the two when talking about e.g. scaling problems.

YMMV, but, outside of technical contexts, the phrase "increased exponentially" is often used by people who don't even know the difference between linear, geometric and exponential growth. In many cases they don't even understand that the word "exponential" refers to a rate of growth, if they've heard of the concept.

Take the context of a high-profile art magazine, Frieze. (I googled "frieze increased exponentially"). This is shooting fish in a barrel—but the most egregious example in the first page of hits is this one:

"Seppie in nero’ – squid in its own ink – is my favourite Venetian delicacy. Although customarily served with polenta, I prefer it on thick spaghetti since pasta exponentially increases the naturally squirmy quality of the creatures’ tentacles, creating a Medusa-like mound of inchoate, salty matter."

So you've got an art critic writing slightly pretentiously about food, and he throws in an "exponentially" which has nothing to do with a rate.

This and similar usages of "exponentially" are extremely widespread now. People talk about exponential increases without any mental model of the rate of growth as a function of time at all—just the woolly idea that something is growing fast.

"The term "exponentially" is often used to convey that a value has taken a big jump in short period of time, but to say that a value has changed exponentially does not necessarily mean that it has grown very much in that particular moment, but rather that the rate at which it grows is described by an exponential function."

https://books.google.ie/books?id=aVovDwAAQBAJ&pg=PA36&lpg=PA...

The battle is lost on this word, as it is with "literally". To the man on the street "exponentially" really just means "a huge amount" now.

There is absolutely a very practical difference.