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"exponentially increasing" is grammatically correct and commonly used in written English to describe a rapid and significant increase in something.
One example of using "exponentially increasing" in a sentence could be: "The demand for renewable energy has been exponentially increasing in the past decade as more countries prioritize sustainable practices."
Exact(58)
One could feel the excitement exponentially increasing after that day.
Since then, the consumer interest and the sales of Grundig appliances have been exponentially increasing.
This was a weapon, deliberately wielded, with an exponentially increasing number of possible sources.
So if it can't be done spatially, better it be done temporally, by exponentially increasing the number of available screenings.
A shortage of asylum officers and judges – a contrast to the Border Patrol's exponentially increasing manpower – further slows proceedings.
In this potential future, exponentially increasing technological change is unstoppable because of the great advantages it confers on its adopters.
Riding the exponentially increasing power of the computer chip, the valley has demonstrated the ability to reinvent itself relentlessly.
The shift resulted in an "exponentially" increasing FBI appetite for email and other records under the Patriot Act provision.
Re "The Nuclear Option": This is a predictable proposal considering the world's shrinking fossil fuel reserves and our ceaseless, exponentially increasing demands for fuel.
The paradigmatic idea was that society under the prophet Muhammad had attained a perfection from which later generations were condemned to live at an exponentially increasing remove.
Harmonic oscillator with exponentially increasing mass.
More suggestions(15)
significantly increasing
strongly increasing
heavily increasing
exponentially rising
greatly increasing
exponentially widening
noticeably increasing
explosively increasing
enormously increasing
substantially increasing
materially increasing
immeasurably increasing
tremendously increasing
considerably increasing
exponentially raising
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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