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The phrase "at a corresponding rate" is correct and usable in written English.
It can be used when discussing the relationship between two variables that change in relation to each other, often in contexts like finance, science, or statistics.
Example: "As the demand for the product increases, the price will rise at a corresponding rate."
Alternatives: "at a proportional rate" or "in a similar manner."
Exact(2)
Although there was much technological progress in the Roman empire and during the Middle Ages, philosophical reflection on technology did not grow at a corresponding rate.
Consequently, the population shadows the moving optimum, changing at a corresponding rate k per generation but lagging behind the current optimum by a quantity k/ R (Charlesworth 1993; Lynch and Lande 1993).
Similar(56)
Patients comprising the efficacy population (n = 81) obtained an 80.2 % response rate at ≥ 50%%, whereas a corresponding rate of 54.6 % was noted in the ITT population.
The GaN flux is maintained at a corresponding GaN growth rate of 16 nm/min.
After baseline variables were obtained, low-dose insulin was infused to achieve normoglycemia, after which insulin infusion was either terminated or, for patients treated with insulin pumps, continued at a rate corresponding to the basal rate of the patient's insulin pump.
For the case with water consumption, water flow converges toward the waste canister at a rate corresponding to the water consumption rate associated with the corrosion reaction.
The cores were set-up to simulate conditions in the unsaturated zone of the UK Chalk aquifer by applying a suction of 1 kPa (0.1 m H2O) to the base of each column, and eluting at a rate corresponding to an average recharge rate through the unsaturated Chalk.
Figure 5 compares the rate distortion performance between nested sampling and coprime sampling, where D is the distortion between the original source and its sparse-sampled representation, and R(D) is the corresponding rate at a particular distortion D. With the same sampling spacings chosen, N1=P, and N2=Q, at the same distortion, the rate of nested sampling is less than that of coprime sampling.
Let us now look at the corresponding rates at outage probabilities 10 and 50%, when the threshold value γ ̂ th (or γ ̌ th ) varies.
Interest, according to Falla and Giraldo, has climbed at a rate corresponding to their success.
These mediator cells (like many in the nervous system) actually act as a sort of analog-to-digital converter, sending signals at a rate corresponding to how much light their selected rods and cones are receiving.
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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