All of those formulas will necessarily have some sort of exponential function in them. But you could express them in any base. Where e specifically comes in handy is if you also want to be able to describe, not only the amount at any given time, but also the rate of change at any given time.
Yes, describing the amount and rate of change over time on exponential growth/decay, where the rate depends on the amount, is the point I was trying to make. And those exponential functions are typically based on the natural logarithm.