1. The Number e Section 8.3

2. WHAT YOU WILL LEARN: 1.How to use the number e as the base of exponential functions.

3. Oh Boy! Vocabulary We have many “ special ” numbers in math. We have pi, i, zero, and we are adding a new one … The number is called the natural base and we use the letter “ e ” to represent this number. This number was discovered by a man named Leonhard Euler

4. The Value of e Evaluate the following on your calculator (use 1.1 for the first number 1.01 for the second, etc):

5. The Value of e Evaluate the following on your calculator (use 1.1 for the first number 1.01 for the second, etc): What number are we “zeroing” in on? e!

6. The Rules of e You simplify expressions involving the natural base using the same rules of exponents we used in the previous chapter: Simplify:

7. You Try Simplify.

8. Evaluating Natural Base Expression - Calculator Evaluate. e 2 e -0.06

9. Graphing Natural Base Functions Graph y = 2e 0.75x State the domain and range.

10. You Try Graph y = -3e 0.5x. State the domain and range.

11. Another Graphing Example Graph y = e -0.5(x-2) + 1. State the domain and range.

12. You Try Graph y = e 0.4(x+1) - 2. State the domain and range.

13. Compound Interest When you earn interest on the principal amount plus the interest already earned, it is called compound interest. Formula: A = Pe rt

14. Homework Homework: page 483, 18-28 even, 34, 36, 50-56 even, 61-66 all, 67, 68, 70, 76