Section+3.11


 * §3.11 Compound Interest; the Number** //**e**//

Mrs. Tyson said that the general rule for logarithms is:

We then explored Euler’s number, known as // e //.



Now we want to look at



Let

If , this implies that by cross multiplication. Since , ,

So, looks a lot like

Now using the rule of exponents we can say that is the same as what we originally had written as

This rule of exponents is the same one that justifies the following:

Now you can “fake it” and move the “limit” part into the parentheses. Mrs. Tyson calls this “faking it” but she says that moving limits and playing with order of operations is legal. Everything in the line below within the parentheses is equal to Euler's number.