So, play this for me.. Which specific profession I should be in for this to matter to me? Not that I should be curious about fundamentals, but something I can apply in a meaningful way?
Finance, economics, ecology, virology, electrical engineering, mechanical engineering, chemical engineering, software engineering, pretty much any field with a technical component (i.e one that uses numbers).
You could reasonably just look at 2^n for software, though in general usually continuous math is simpler then discrete math IMO. Doubling vs. e^x is kind of an exception to the rule, and if you do any software involving signal processing or simulations, you'll want to understand the continuous version.
Everyone has use for understanding and detecting exponential processes. And the most important and easiest to identify part of exponential processes is the derivative, their rate of change is proportional to their value.
It is like understanding basic dice outcomes, everyone should know that since it is so basic to understanding events that happens in the world, political discussions and advertisements and products.
