I am writing up a small text about (increasing) exponential functions versus linear functions. I want to make the point that it is not true that if an exponential is bigger than a linear function that it will not always stay that way.
To make my text more readable, I want to label the images with some relatable things that grow exponentially versus linearly. Now, I have two problems: First, I have a really, really hard time to think about things not covid-related. Secondly, I want to have an example where we want the exponential growth to exceed the linear growth.
I have thought about repopulation of depleted environments, but the examples feel forced. Interest on a bank account is certainly "good" exponential growth, but I do not see a natural linear growth for comparison.
So, do you have very common recognizable examples of exponential versus linear growth where we are happy that the exponential growth exceeds the linear one?