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The phrase "at an increasing rate" is correct and usable in written English.
It can be used to describe a situation where something is happening more frequently or intensively over time.
Example: "The population of the city is growing at an increasing rate, leading to concerns about infrastructure and resources."
Alternatives: "at a growing pace" or "at an accelerating rate."
Exact(60)
The Greenland ice sheet is losing mass at an increasing rate.
Ice sheets are melting at an increasing rate and sea level rise was is accelerating.
"Glaciers are melting at an increasing rate and the Himalayas are definitely warmer.
Former agricultural land near large cities has been converted to urban use at an increasing rate.
Today these promises are gutting the state budget, and will do so at an increasing rate.
"Maritime archeological sites, finite and irreplaceable, are being disturbed and, in some cases destroyed, at an increasing rate.
The universe is expanding at an increasing rate, and the reason may be a force from another universe.
Rugby, on the other hand, is heading in the opposite direction at an increasing rate of knots.
The state's provision of many of these goods – notably transport, education, housing and healthcare – is being privatised or outsourced at an increasing rate.
Although enthusiastically supported by the major parties, the fact is they continue to plunge families into penury at an increasing rate.
Innovations in fuel cells, fuel itself, composites and materials, manufacturing processes, etc. are being translated into our vehicles at an increasing rate, all in the name of efficiency.
More suggestions(12)
at an optimised rate
at an uncontrollable rate
decline at an increasing rate
declining at an increasing rate
disappearing at an increasing rate
fall at an increasing rate
at an increasing level
at an increasing frequency
at an increasing proportion
at an increasing speed
at an increasing pace
at an augmented rate
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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