I think it would look more like a root-function, which increases rapidly early on but slows down the better you get.
But your fears of improvement having come to a halt might put you into a mindset that will make that fear come true.
Plateau
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I'm talking only about my experience. As a chess player, I have reached a point where I can't advance any further if I don't study chess theory. I'm working on it, but progress is slow and tough. On the contrary, getting a 1500-1600 Chess.com rating has been a quite natural and effortless process to me.
In my case, joining an OTB club 1 year ago also has helped.
I need to modify my statement. I think that there is a plateau if you try and keep improving in the same way. If there is an area of the game you have not worked on, then that might be the way forward and so on.
I think there's certain steps that sooner or later have to come in order to allow further progress.
One of the most promising and difficult sounding ones is the step of visualization. Where you can "see" a game by just reading the notations.
When we start playing chess, our improvement is very rapid. And it goes on like that for the first year. However, is there a plateau that we hit in terms of skill or is it just a matter of shifting gears and start practicing and studying in a different way. If someone has succeeded in pushing past their plateau then please let me know as I am struggling to improve.