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The phrase "an increased rate" is correct and usable in written English.
It can be used when discussing a rise or growth in frequency, speed, or quantity of something.
Example: "The company has reported an increased rate of production due to higher demand for its products."
Alternatives: "a higher rate" or "an elevated rate".
Exact(60)
All salaried Greeks pay their taxes and continue to do so at an increased rate.
Patients with transplant glomerulopathy showed an increased rate of graft loss after biopsy.
"This results in an increased rate at which [posts from antisocial users] are deleted," they say.
One study found an increased rate of atrial fibrillation among moderate drinkers.
Post reaction, the Co nanoparticles were carburized at elevated pressure, demonstrating an increased rate of carburization compared with atmospheric studies.
When parts of the brain are activated, brain cells begin to metabolize glucose at an increased rate.
Heart abnormalities, for example, occur at an increased rate in individuals born with cleft palate.
Laser therapy in patients with skin of color is associated with an increased rate of complications.
In rural United States, however, an increased rate of asthma has been found among schoolchildren.
No effect was found on wound healing, but we found an increased rate of hair regrowth.
Most ganglion cells showed an increased rate; some cells, however, showed decreased activity during illumination.
More suggestions(18)
an increased tempo
an increased price
an increased coefficient
an increased index
an increased speed
an increased frequency
an increased pace
an increased percentage
an increased ratio
an increased velocity
an increased level
an increased prevalence
an increased tariff
an increased awareness
an increased remoteness
an increased supply
an increased workload
an increased role
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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