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The phrase "absorb a finite amount" is correct and usable in written English.
It can be used in contexts discussing limits or capacities, such as in science, engineering, or economics.
Example: "The material can absorb a finite amount of energy before it begins to degrade."
Alternatives: "take in a limited quantity" or "acquire a restricted amount".
Exact(1)
(I05) The limits of knowledge Bounded rationality implies that humans can absorb a finite amount of information before reaching saturation and becoming overwhelmed [2].
Similar(59)
"There is a finite amount of shopping dollars out there, and if Wal-Mart is absorbing a huge percentage of them, they aren't left for the other retailers," said Richard Lipsky, a lobbyist for local businesses who is fighting Wal-Mart.
"There's a finite amount of time.
"There's a finite amount of water," she said.
There isn't a finite amount of soil.
ME: Because there's a finite amount of land.
There is only a finite amount of usable resources.
The trouble is, there's a finite amount of it".
"So there is a finite amount of time," he said.
First, we should understand that there is a finite amount of radioactive material at these plants.
"The party has a finite amount of money," one national official said.
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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