The phrase "a rapidly increasing" is correct and usable in written English.
It can be used to describe something that is growing or rising quickly, often in contexts related to statistics, trends, or phenomena.
Example: "The city has seen a rapidly increasing population over the last decade."
Alternatives: "a fast-growing" or "a swiftly rising".
The pressure on our global water supplies has been growing alongside a rapidly increasing human population.
A rapidly increasing population is not clearly either an advantage or a disadvantage to economic growth.
And a rapidly increasing number of countries, including Pakistan, Philippines, Malaysia, Tunisia and Vietnam, are developing their own MPIs.
With a rapidly increasing world population and increasingly precarious agricultural production, some NGOs consider the food system to be broken.
Tents or boards are indispensable for shelter for the well and the sick — a rapidly increasing list".
A rapidly increasing population and the free import of consumer goods swiftly ate into earnings from foreign trade.
Though those papers may be losing sales at a rapidly increasing rate, there is not the slightest sign of them relinquishing their influence.
Mr. Hairr said village trustees authorized the hunt in October to reduce a rapidly increasing population of more than 40 deer that had become a hazard to drivers.
Despite the reluctance of some executives and franchises to hire Europeans, a survey of league rosters suggests a rapidly increasing diversification.
Below that, a rapidly increasing number calculates how many hundreds of thousands have "landed in Gina's pocket" since you landed on this Web site.
Combining guitar distortion, anguished vocals, and heartfelt, angst-ridden lyrics, Nirvana and Pearl Jam won a rapidly increasing audience, moved to major labels, and released multimillion-selling albums.
