The phrase "a relentlessly growing" is correct and usable in written English.
It can be used to describe something that is continuously increasing or expanding without pause or limitation.
Example: "The company is facing a relentlessly growing demand for its products, which has led to increased production efforts."
Alternatives: "an ever-increasing" or "a continuously expanding".
A relentlessly growing deficit of opportunity is a bigger threat to our future than our rapidly shrinking fiscal deficit.
Fish farming proponents contend that aquaculture is the only way to meet the food demands of a relentlessly growing world population, due to double in another 60 years.
In Paul Krugman's Dec. 6th New York Times opinion piece, "Obama Gets Real" he notes that "a relentlessly growing deficit of opportunity is a bigger threat to our future than our rapidly shrinking fiscal deficit".
In that event, preventing a dynastic society of relentlessly growing inequality would require large-scale redistribution.
Doing such an inventory has little short-term payoff, and is, as Amsterdam CTO Baron puts it, "a boring, boring job". But successful analytics projects depend on solid infrastructures and thorough data, and on building a process to keep up with the (relentlessly) growing data supply.
President Obama recently declared that the "relentlessly growing deficit of opportunity is a bigger threat to our future than our rapidly shrinking fiscal deficit".
"Traffic has been relentlessly growing in part because land use has developed in a way that is totally automobile oriented," said Jeffrey M. Zupan, senior fellow for transportation at the Regional Plan Association, a nonprofit planning group based in New York City.
Its relentlessly growing menace is absolutely captivating and morbidly fascinating......................
The current harvest falls well within the agreed upon 5 million metric ton limit, but the commercial appetite is relentlessly growing.
That has sparked hopes that unlocking those resources could help meet China's relentlessly growing energy demand and ease its reliance on heavily polluting coal-fired power plants.
For there would be every chance that, the better Russia came to understand the implications of China's relentlessly growing economic and military might, the more frightened of China it would become.
