Warm-up

1. Warm-up Simplify the expressions.

2. Use Functions involving e EQ: When is the natural base e useful? Mastery demonstrated in summary of notes and in practice problems.

3. The natural base e or the Euler number is a special number like Example 1 Simplify the expressions. a. b. c. EQ: When is the natural base e useful? Mastery demonstrated in summary of notes and in practice problems.

4. a. e4 b. e –0.09 0.09 Example 2 Evaluate natural base expressions Use a calculator to evaluate the expression. Expression Keystrokes Display 54.59815003 0.9139311853 EQ: When is the natural base e useful? Mastery demonstrated in summary of notes and in practice problems.

5. EQ: When is the natural base e useful? Mastery demonstrated in summary of notes and in practice problems.

6. Example 3Graph the function. State the domain and range. a. b. EQ: When is the natural base e useful? Mastery demonstrated in summary of notes and in practice problems.

7. EQ: When is the natural base e useful? Mastery demonstrated in summary of notes and in practice problems.

8. Finance You deposit $4000 in an account that pays 6% annual interest compounded continuously. What is the balance after 1year? EXAMPLE 5 Example 4 Model continuously compounded interest EQ: When is the natural base e useful? Mastery demonstrated in summary of notes and in practice problems.

9. GUIDED PRACTICE FINANCE:You deposit $2500 in an account that pays 5% annual interest compounded continuously. Find the balance after each amount of time? a. 2years b. 5years c. 7.5years EQ: When is the natural base e useful? Mastery demonstrated in summary of notes and in practice problems.

10. Write your Summary to the Essential Question: When is the natural base e useful? Homework: p. 495 - 496# 3, 7, 11, 15, 16, 17, 19, 23, 27, 31, 35, 39, 42, 45, 48 (All the problems on the left-hand side of pages.)

11. Simplify the expression.