1. 4.3 Use Functions Involving e PROJECT DUE: Tomorrow 4.1-4.2 Quiz: Tomorrow Performance Exam: Friday *We will be having a book check tomorrow…. BRING BOTH BOOKS TOMORROW!

2. Vocabulary The number denoted by the letter e is called the natural base e or the Euler number. –Think of e like you do π –e is approximately 2.718281828. A function of the form f(x) = ae rx is called a natural base exponential function.

3. Natural base exponential function f(x) = ae rx –If a is positive and r is positive OR if a is negative and r is negative: GROWTH –If a is positive and r is negative OR a is negative and r is positive: DECAY

4. Example 1: Simplify the expression a) e 6 e 4 = b) c) (-2e x ) 3 =

5. Example 2: Graph the function. State the domain and range. a) y = 4e -x + 5

6. Example 2 cont’d: Graph the function. State the domain and range. b) y = e 2(x+1) - 2

7. Example 3: A population of bacteria can be modeled by the function P = 70e 0.22t where t is the time (in hours). Estimate the population after 4 hours.

8. Vocabulary Continuously Compounded Interest –When interest is compounded continuously, the amount A in an account after t years is given by the formula A = Pe rt. P is the principal r is the annual interest rate expressed as a decimal.

9. Example 4: You deposit $500 in an account that pays 3% annual interest compounded continuously. What is the balance after 2 years? A = Pe rt

10. Homework P. 142 #1-28 (Green book) Finish Project –Email to Maggie_Chapman@gwinnett.k12.ga.us Study for 4.1-4.2 Quiz, and Performance Exam BOOK CHECK TOMORROW!