Stop using e for compound interest

To me it was only when we got to radioactive decay in physics it clicked to me why the particular "e" was special and useful. Background: exp(x) was introduced as the inverse to log(x), defined as the area under 1/x etc. It was already in 1st high school year (before integrals had been introduced!). We showed how you could express other bases as e^(ax) but you could have done that with any other base, so nothing special about e. In calculus we later learned that exp'(x) = exp(x). This made it clear it was special - but not why it was useful.

The clear usefulness appeared in the case of radioactive decay. We first learned about half-life, and clearly you can write the decay function as N(t) = N0 * 0.5^(at) with 1/a being the half-life. But we then learned that the decay values in the data book are often not the half-life but this special "k" that you put in a decay equation that has e as the: N(t) = N0 * e^(-kx). My reaction was: why did they pick e here? Why not just use 0.5 as base and the book would list the half-life? But then we got to the kicker: we learned the formula: Activity = -k*N, meaning that the activity (decays/time-unit) is proportional to the amount of material with k being the proportionality constant. We hadn't learned of differential equations yet and I was confused about what k was, having first seen it in the decay equation and now in the activity equation which were seemingly very different... how on earth could the same number work in both capacities. And I read a bit ahead in the math book and it all made sense. And then I understood it was because of e as the base that the constant k got this property - which it would only get in that particular base. So this showed to me how e was special, allowing the same constant to serve in these two capacities.

The compound-interest intro to e (the value of 1 dollar compounded continuously for a year at 100% interest), to me, has several useful advantages over different introductions that are more mathematically rich:

- It's elementary to the point that you can introduce it whenever you want.

- It automatically gives a sense of scale: larger than 2, but not by a lot.

- At least to me, it confers some sense of importance. You can get the sense that this number e has some deep connection to infinity and infinitesimal change and deserves further study even if you haven't seen calculus before.

- It directly suggests a way of calculating e, which "the base of the exponential function with derivative equal to itself" doesn't suggest as cleanly.

I don't know of any calculus course that relies on this definition for much: that's not its purpose. The goal is just to give students a fairly natural introduction to the constant before you show that e^x and ln x have their own unique properties that will be more useful for further manipulation.

Uhhh, maybe I am missing something here, but: why not?

> …so it is hard to explain why their kids would be better off knowing something they don't need.

Math is full of extremely useful concepts that aren’t otherwise obvious. To me, it’s less about “I’m going to need to use this equation” and more about “This is a pattern I will encounter throughout the world.”