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The phrase "affects the rate at" is correct and usable in written English.
It can be used when discussing how one factor influences the speed or frequency of another factor.
Example: "The temperature affects the rate at which the chemical reaction occurs."
Alternatives: "influences the speed of" or "modifies the frequency of".
Exact(21)
The concentration affects the rate at which reacting molecules collide, a prerequisite for any reaction.
Unless you have the constitution of a rhinoceros, you can probably notice how alcoholic strength affects the rate at which you begin to feel tipsy when drinking.
This heating prevents the gas from cooling, and affects the rate at which new stars form, thereby limiting the size of the central galaxy.
In the purest test of reasoning, pupils were shown a pendulum and asked how to find out what affects the rate at which it swings.
Pore size is an important parameter for absorbent materials as it affects the rate at which a fluid flows into or through a capillary network.
In the case of lactic acid solutions, the ratio of lactate ions to non-ionized lactic acid affects the rate at which both pass through nanofiltration membranes.
Similar(39)
Within these contexts, alcohol use affects the rates at which problems will occur.
Most studies are deterministic, but uncertainty will also affect the rate at which future levels of climate damage are discounted17,18,19,20.
The old wind-chill charts were based on research in Antarctica in 1945, when scientists measured how wind affected the rate at which water froze.
The quantity and composition of what is available can affect the rate at which ecosystem processes progress.
The kinesin cycle therefore contains at least one load-dependent transition affecting the rate at which ATP molecules bind and subsequently commit to hydrolysis.
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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