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"had grown at" is a grammatically correct phrase and can be used in written English.
It is typically used to describe something that had experienced growth or progress over a period of time in the past. It is usually seen in past tense sentences, where the past perfect "had + past participle" is used. Example: The company had grown at a rapid pace over the past five years, expanding into new markets and increasing its revenue by 50%.
Exact(60)
The industry had grown at an annual rate of 3.7%.
And I understood how much my children had grown at New Humanitarian.
During the previous five years it had grown at around 3.5 per cent.
Between 1987 and 1991, EDC's foreign sales had grown at an annual rate of over 80%.
Between December 1994 and December 1996 Internet traffic had grown at an unthinkably rapid rate.
Yet the economy had grown at more than 6% a year since 2004, and poverty had fallen faster than ever.
A study last year found that ridership on the L had grown at three times the systemwide rate since 1998.
Still, the latest data showed the economy had grown at its fastest pace in nearly two years.
If productivity had grown at the higher rate all along, national income would be 30percentt greater today.
Couscous sales for Near East, which in 1999 had an 86percentt market share, had grown at a miraculous pace.
For the five years before June 30, the endowment had grown at an annualized rate of 17.3percentt.
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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