*The natural base is e = 2.71828…*

The function *f*(*x*) = e^{x} is the natural exponential function.

*Domain: all the reals*

*Range: y>0*

*y-intercept: (0,1) *

**Compound Interest Formulas**:

*After t years, the balance A in an account with principal P and annual interest rate r (expressed as a decimal) is given by the following formulas:*

**1. For n compoundings per year: A** = **P**((1 + r/n)^{nt}) .

Example: You want to invest $500 for 3 years in a bank. They offer you the following choices, which do you take?

1. 3% interest compounded 4 times a year

2. 4% interest compounded 2 times a year

3. 5% interest compounded 1 time a year

**2. For continuous compounding:** **A** = **P**e^{rt}.

Example: You have a credit card with $2000 on it. Your interest is 15.4%. How much interest will you have paid on it by the end of the year?… by the end of 2 years?

*Homework #26 pg. 225; #35, 39, 43, 47, 51, 53, 59 - 69 odd, 73, 76*