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The phrase 'the rising rate' is correct and can be used in written English.
You can use it to describe a trend of increasing or growing numbers (e.g. The rising rate of unemployment has been a major concern for governments around the world).
Exact(60)
Both Santorum and Romney cited statistics about the rising rate of births to single mothers.
But officials said yesterday that, viewed in that context, the rising rate was not alarming.
The rising rate of obesity among teenagers is producing symptoms hitherto unseen in children.
And the rising rate in the initiating vessel is slower than that in the secondary vessel.
The rising rate of electrical conductivity (EC) was 130 μs/cm per day.
Charities blamed welfare cuts and rising housing costs for the rising rate of evictions.
But the rising rate of obesity in the United States is narrowing the gap for the general population.
Still, some economists said the rising rate of savings was a natural reaction, penance for America's spendthrift ways.
Meanwhile, the rising rate of maximum pressure and the volume of the vessel meet the cube root law.
Mr. Blitzer pointed to the rising rate of credit card defaults as a reason to worry about the economy.
In some ways, the results represented a ray of hope when governments and doctors are struggling to control the rising rate of diabetes worldwide.
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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