I almost always type it out long form exp(x), but some people like to use e^x. I guess they don't see the point in typing 6 characters when 3 will work
. My method makes it more readable when you have exp(x^2) as e^(x^2) gets really tiny.
I have never seen a spreadsheet or calculator that will take e by itself and make it a formula.
They may have a button on a calculator for e^x, but that's a function, not an e by itself. The TI84 has a separate e key (2nd divide) that will give you e by itself, just like pi, they're both constants. If you type =e in Excel, you get a #NAME? error. Same thing for =pi. You need =pi() and =exp() in Excel. Desmos might do something non-standard -- no, you just type e and you get the constant. Same thing with web2.0calc.com, it just treats e as a constant. In Maxima, you can type out exp(x) or use %e^x (and the constant pi is %pi there as well).
Your need for e may vary depending on what you teach. I teach a differential equations class where most of the class is spent dealing with solutions involving e to some power. But you're right in that I don't ask my students to give me 2.718^(2t), I just write it as e^(2t).
I would have been okay with with making this one be exp() and use exp(1) if you want the value of e. That's part of why I don't like Canvas putting it under the "helper functions" as it's not a function, it's a constant. But I guess they didn't want a separate document for "helper constants" with just two things in it.
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