"The number of lily pads on a pond double every day. If it takes 20 days for the lily pads to completely cover the pond, how long does it take to cover half the pond?"

I think you will be surprised by how many people say "10 days."

So if you explain to the politician, once you start getting cases in your country and give them the actual growth rates, and what slowing down the growth rates will mean, with nifty charts and so forth.

Like maybe they should do in the movie Outbreak where they have display of the red spreading across the country on its way to the White House, with a timeline animated below it, then the politician will understand the situation without intuitively understanding exponential growth.

I suppose reasonably competent data visualizers who have ever had to explain complicated things to non-technical people in an important meeting would know how to represent the concept in their particular domain without much problems.

on edit: changed our to your

Why is it relevant that people don’t correctly apply exponential reasoning automatically? Because when people encounter information in everyday life (outside of the specific job they’ve been trained to do) they tend to use intuitive thinking predominantly. This matters a hell of a lot when it comes to making political decisions of a technical nature, such as infectious disease planning and response. Lo and behold, this is the exact problem the Italians are trying to warn everyone about!

Relating this to the spread of the virus, people aren't carrying around an animation of this in their minds. Perhaps science communicators should do a better job of communication and produce such an animation? But then you're still not getting people to understand the concept. You're telling them "this is what it looks like, sort of, now just trust us." The problem is that people don't trust scientists (and mathematicians) as it is.