R Hansen says: >Maybe they learned about exp from Desmos. :)
You know you may have a very good point there. Line graphs may help one explore such functions, but they can also be very misleading.
Perhaps a better way to look at exp early on (on whole numbers, say) is to look at differences between successive terms of the sequences n^2 and 2^n. I think one could look at that in grade school, but I was never exposed to such thinking early on. It could also make a very nice animation ;-)