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The phrase "they projected" is correct and usable in written English.
It can be used when discussing forecasts, estimates, or predictions made by individuals or groups regarding future events or outcomes. Example: "Based on the current trends, they projected a significant increase in sales for the next quarter."
Exact(58)
Just as disturbing as the projections themselves is the notion that companies are actually spending less than they projected for the current quarter.
"They projected 91 units.
Eventually, they projected Mr. Paul to be in third place.
They projected those fears onto one demographic: young, black males.
"They projected 'fill' rates that were overly ambitious," she said.
They projected an air of physical strength that most women can relate to.
They projected Banuelos as a future ace, and so far he has fulfilled their expectations.
A year ago they projected growth of about 4% this year and next.
They projected an image of a giant crack forming across the building's facade.
When Mr Putin came to power in 2000, they projected their views onto the whole country.
They projected freedom as America's only story in a harsh world.
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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