Nice examples of limits to infinity in real life

I have to teach limits to infinity of real functions of one variable. I would like to start my course with a beautiful example, not simply a basic function like $1/x.$ For instance, I thought of using the functions linked to the propagation of covid-19 and show that, under the basic model, the number of contaminations will go to $0$ when time goes to $+\infty.$ However, this is a bad idea because the model is not so easy to explain and moreover students are sick of covid-subjects.

Hence, I ask you some help to find interesting examples from physics, geography, etc ... I suppose that an example with "time" going to $+\infty$ would be nice.

Solution 1:

"John Napier" and how he get to "e=2.7182818284..." might be a good real life limit. (https://en.wikipedia.org/wiki/E_(mathematical_constant) )

Solution 2:

Explaining the failure of Zeno's Paradox could be a cool activity. Motion can be broken down into so many very small parts, namely steps of length $1/2^i$. Show the fact that $\lim_{n \to \infty} \sum_{i=1}^n 1/(2_i) =1$. The only prerequisite of this is understanding geometric series.

I would also suggest compound interest and its limiting case of continuous compounding, as a previous poster suggested.