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"exponentially increase" is a correct and usable phrase in written English.
It can be used when describing a quantity that is growing or increasing in an extreme or rapid fashion. For example: "The demand for the product has exponentially increased over the past year."
Exact(59)
But did it exponentially increase my love of the opera?
They were engineered in such a way that they could exponentially increase profits but would, also, exponentially increase losses.
If we neglect prevention, the need for treatment will exponentially increase.
"The rumors will exponentially increase every day until the Fourth of July," Mr. Gray said.
This could exponentially increase the amount of science done across the globe".
But computerized databases are expected to exponentially increase the number of matches, as they did with fingerprints.
"Studies demonstrate unequivocally that free cocktails exponentially increase the chance of violence in arguments about feminine agency," he says.
The race for mayor will soon exponentially increase the tonnage of blather.
A park would "exponentially" increase surrounding property values, generate greater tax revenue and benefit the TIF district.
As the novelist Hari Kunzru has observed, a Nobel citation can exponentially increase a writer's audience and help keep independent publishers afloat; in 2016, that opportunity was lost.
"The company needs to exponentially increase or supercharge the growth of their Internet revenues," a person briefed on the funds' plans told The Times.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com