1. Compute interest on an account that is continuously compounded. Slide 1 OBJECTIVES

2.  limit  finite  infinite  continuous compounding  exponential base (e)  continuous compound interest formula Slide 2 Key Terms

3.  Can interest be compounded  Daily?  Hourly?  Each minute?  Every second?  If $1,000 is deposited into an account and compounded at 100% interest for one year, what would be the account balance at the end of the year? Slide 3

4. Given the quadratic function f(x) = x 2 + 3x + 5, as the values of x increase to infinity, what happens to the values of f(x)? Slide 4

5. As the values of x increase towards infinity, what happens to the values of g(x) = –5x + 1? Slide 5 CHECK YOUR UNDERSTANDING

6. Slide 6 Given the function f(x)=, as the values of x increase to infinity, what happens to the values of f(x)?

7. Slide 7 If f(x)=, use a table and your calculator to find f(x). CHECK YOUR UNDERSTANDING

8. If you deposited $1,000 at 100% interest, compounded continuously, what would your ending balance be after one year? Slide 8

9. The irrational, exponential base e is so important in mathematics that it has a single- letter abbreviation, e, and has its own key on the calculator. When you studied circles, you studied another important irrational number that has a single-letter designation and its own key on the calculator. The number was π. π = 3.141592654… e = 2.7182818281828… Continuous Compounding formula: B = pe rt Slide 9 CHECK YOUR UNDERSTANDING

10. If you deposit $1,000 at 4.3% interest, compounded continuously, what would your ending balance be to the nearest cent after five years? Slide 10

11. Craig deposits $5,000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent? Slide 11 CHECK YOUR UNDERSTANDING