1. Pre-Calculus 5-4 The number e To define and apply the natural exponential functions.

2. Compound Interest: interest evaluated more than once over a time period.

3. Natural Base e

4. The number e is irrational – its decimal representation does not terminate or follow a repeating pattern.

5. As n approaches infinity, the compound interest formula approaches the formula for continuously compounded interest: A = Pe rt

6. Using a calculator Evaluate e 2 using a graphing calculator Locate the e x button you need to use the second button 7.389

7. Evaluate e -.06 with a calculator

8. Suppose you invest $50.00 at 6% annual interest. Calculate the amount that you would have after one year if the interest is compounded: a.quarterly b.monthly c.continuously

9. Examples 2: When Saige was born her grandparents started a college fund. They deposited $3,000 into a college savings account paying 4% interest compounded continuously. a) Assuming there are no deposits or withdrawals, what will the balance be after 10 years? A = 3,000e (.04*10) A = $4,475.47

10. b) How long will it take to reach a balance of $15,000 y = 3,000e (.04x) y = 15,000 Find the intersection. It would take 40.24 years.

11. c) If the goal of her grandparents was to reach $10,000 by her 18 th birthday, what should the initial deposit have been? 10,000 = Pe (.04 * 18) Should have deposited $4868.55 10,000 = P(2.054)

12. Homework: Finish the 5.4 Worksheet