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The phrase "a rather constant rate" is correct and usable in written English.
It can be used when describing a situation where something is occurring at a steady or unchanging pace.
Example: "The population of the city has been growing at a rather constant rate over the past decade."
Alternatives: "a fairly steady rate" or "a relatively stable rate".
Exact(2)
The LAGs are relatively evenly spaced, indicating cyclical growth at a rather constant rate.
During the course of the experiment these extinctions occurred at a rather constant rate of approximately 1.25 clonal extinctions per bottleneck and the mean time to extinction of the 20 replicate lines was 8.55 ± 4.07 bottlenecks.
Similar(58)
Based on Amprino's Rule (e.g., [ 75, 76]), this bone grew at a relatively high and rather constant rate.
Some channels exhibited a significant decline of sedimentation rates through time, whereas others maintained rather constant rates.
Interestingly, the positivity-rate by FISH when using this assay as the primary test in our institution (n = 4843), resulted in a rather constant positivity-rate prior to and after applying the modified ASCO criteria.
Small necrotic foci were a rather constant feature.
As illustrated by Figure 2A, such a transformation implies that recurrence-free survival decreases with each additional positive node, but at a declining rather than a constant rate.
Processing power grows every year at a constant rate rather than by a constant amount.
In contrast, in postmenopausal patients trastuzumab was rather used on a constant rate of 49.1% from 2006 to 2011 after a first augmentation from 30.4% in 2006 to 53.8% in 2007.
The ellipsometric data show that thinning of the oxide film in H2SO4 at open-circuit occurs by uniform dissolution at a constant rate, rather than by localized attack.
But the growth of the number of susceptible individuals is governed by a constant rate rather than the logistic function.
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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