You just described Sigmoid curves, roughly speaking. The only issue is your incorrect use of "exponential".

The idea is that it's not exponential for two main reasons:

1. It caps at 100%. You can't grow infinitely.
2. You also need to consider the reverse: going the other way, going from 99% to 98% is a ~1.01% decline. Going down from 2% to 1% is losing half your remaining users. That's huge.

Exponential growth is used colloquially for any situation where there's an upward curve to the trend; in calculus terms, the second derivative is positive. But there are a lot of functions with that property, and exponential functions are only 1 type. Sure, it's a common one, but so is parabolic, cubic, and other polynomial functions; a variety of trigonometric functions (over certain domains, like sine from -1 to 0); rational functions (again, over certain domains), etc.

Sigmoid curves (colloquially known as S-curves) are very common in any situation where there's both a contagion factor (like popularity, word of mouth, network effects, etc.) and a limit on growth or maximum carrying capacity. The later is always the case when your function maps to percentages of a population since it caps at 100%.