Explaining e

I wanted to post some insights about e that have clicked between this course and a book I’m using as a companion to this course, called Math, Better Explained. It’s the book I wish I’d had as a frustrated kid trying to understand math (wish I’d had this course, too, instead of the hours upon hours of drudgery I was forced into, but I digress.)

e is “the base amount of growth shared by all continually growing processes.” It’s the base unit of growth; every growth rate can be considered as a scaled version of e, just like every number can be considered a scaled version of 1, and every circle can be considered a scaled version of a circle with a radius of 1, etc. You can see this in the graph from the lesson: if you scale e upwards enough you get to y = 3^x, and if you scale it down, you can get to y = 2^x.

Even cooler, e acts as a kind of speed limit on continuous growth, whether in nature (like multiplying bacteria) or in your bank account. If you had 200 bucks growing with compound interest at 100%, your growth rate would be 200e. It’s a natural constant, like c, the speed of light, which is (probably) impossible to surpass, even in theory.

Please correct any errors I’ve made, I’m just trying to express these insights so that they’ll click more for me and hopefully other people. Cheers!

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Great explanation @Ajai_Raj, this is a good way of looking at it.

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