People are used to arithmetic increase, and I suspect that is what they are intuitively imagining when they think of growth at all. Unless one is used to playing with numbers, we don't well understand geometric growth, let alone exponential. Note: In journalism and everyday conversation, geometric and exponential growth are sometimes used synonymously. "Exponential" is used more frequently because it sounds more impressive. They are not, but it doesn't much matter in discussing something like C19. The point is to understand that something may not look like it is growing very much, but in fact is dangerously explosive.
We think along that red line for most things. The expansion of an epidemic is more like the blue, or even the green line.
An analogy that might help people understand how C19 can be both containable and also quite dangerous is flame and fuel, like charcoal briquettes. If the briquettes are not touching, they will not continue burning long. You can have a box of match flames and not get much going. but if they are touching, and especially if they are stacking in a pile, a single small flame can set them all off quickly. We isolate in order to keep the briquettes from touching each other.