1. Graph Horizontal Asymptote: y = -1 Domain: Range:y > -1 all real numbers a = ____ 2 b= ____ 3 h = ____ 2 k = ____

2. Objective: (1) Using The Natural Base e (2) Using e in Real Life CA Standards: 12.0 Students know the laws of fractional exponents, understand exponential functions, and use theses functions in problems involving exponential growth and decay. Agenda: 02/26/15 1.) Warm-up 2.) Questions: WS Exponential Decay Practice A/B 3.) Lesson: 8.3 The Number e TB 4.) Class/Homework: TB 8.3 5.) Work with Your Neighbor STAY ON TASK!!! 6.) Quiz: 8.1, 8.2, & 8.3 Friday 02/28/15

3. 8.3 The Number “e” Named after its discoverer, Leonhard Euler (Oiler) He lived from (1707 – 1783) History has taught us special numbers: Counting Numbers, Zero, Negative numbers, π, and Imaginary numbers. One of the most famous numbers of modern times is “e. ” This number is called the “Natural Base e.” Let us explore this number using the calculator.

4. 1. Let us analyze the following the table. n1010010001000010000 0 100000 0 2. What value does seem to be approaching as “n” becomes larger? 2.593 74 2.704 81 2.716 92 2.718152.71827 2.71828 2.718281828459…

5. Ex. 1 Simplify. 1) 3) 4) 2) You Try!

6. Ex. 2 Graph Y – Int.: (0,3) HA: y = 0 Domain: All Real Numbers Range: y > 0 Exponential Growth because the coefficient of the x is POSITIVE.

7. Ex. 3 Graph Y – Int.: (0,4) HA: y = 0 Domain: All Real Numbers Range: y > 0 Exponential Decay because the coefficient of the x is NEGATIVE.

8. Ex. 4 You deposit $1,000,000 in a savings account that pays 7% annual interest compounded continuously. What is the balance after 5 years? Write this

9. HOMEWORK Page 483:4 – 80 All