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The phrase "growing geometrically" is correct and usable in written English.
You can use it to describe an increase in something that is happening very quickly or is increasing exponentially. For example, "Since the invention of the internet, the world's access to information has been growing geometrically."
Exact(6)
According to Unaids, South Africa has more than four million infected, and the epidemic is growing geometrically.
The warmth and sun of the past week has re-awakened the endives, growing geometrically and mathematically from their dark centres.
Ultra-Orthodox Satmar Hasidic Jews predominate in the village; many of them moved there from Williamsburg, Brooklyn, beginning in the 1970s to accommodate a population that was growing geometrically.
Outsourcing is not new, but its globalization is growing geometrically.
Goodell's losing streak in the courtroom has been extended, and the list of mistakes seems to be growing geometrically.
But if extinction is avoided, the population rebounds, growing geometrically at a rate FWRR≍ F that can be quite high for well-fed insects (Fig. 1A).
Similar(54)
That is why the numbers grow geometrically," Mr. Vergara said.
In the last five years, the Phoenix restaurant scene has grown geometrically.
The fire grew geometrically in the space of a few seconds.
His basic theory was that populations, which grow geometrically, will inevitably outpace food production, which grows arithmetically.
"They grow geometrically," said Mr. Martin, a former commercial beekeeper and researcher with the Carl Hayden Bee Research Center for the United States Department of Agriculture in Tucson.
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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