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The phrase 'showed a continuous increase' is correct and usable in written English.
You can use it to describe a situation in which a trend or amount increases steadily over time. For example, "The number of members in the local running club showed a continuous increase over the last 5 years."
Exact(30)
With niobic acid, the method showed a continuous increase in the hydronium ion concentration with the number of water molecules.
The scanning electron microscopy images also showed a continuous increase in cell densities during a 6 day incubation on 13 93 glass fiber rafts and scaffolds.
The ionic release profile of Ca2+, PO3−4, Mg2+ and Ti4+ showed a continuous increase in concentration over all immersion times for both testing solutions.
The lattice constant of Cr1−xTixN showed a continuous increase with increasing TiN concentration, and so did the hardness and grain growth rate; the electrical resistivity continuously decreased.
The measured wavelength of the optical absorption spectrum peak maximum λmax showed a continuous increase with increasing chain length up to lengths of nearly 5000 repeat units.
In contrast, in chilled fruits from plants treated with GB, CO2 also remained low during the first 4 days, but from Day 5 onwards, it showed a continuous increase reaching values of 70 ml CO2 Kg−1 hr−1 by Day 9 after being harvested (Figure 3B).
Similar(30)
"Fuel", "application(s)", "oxide", "treatment", "modified", and "nanotube(s)" showed a continuous increasing trend in titles, while the terms "solution(s)" showed a decreasing trend.
The results showed a continuous increases and reassuring trends in the number of HIV literature production from Nigeria.
Similarly, our results showed a continuous increased risk of gout with increasing BMI as well as a protective effect in individuals with a BMI under 20 kg/m.
These data showed a continuous increasing in the response of patients rate during the induction period; at week 10, complete clearing of skin lesions was observed in approximately a quarter of infliximab-treated patients.
Our findings are in line with similar studies showing a continuous increase in joint replacements in past decades, and forecasting a continued increase in demand in the future.
More suggestions(13)
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showed a continuing increase
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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