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Exponential Growth and Decay with the Natural Number "e

This lesson focuses on exponential functions and the natural base "e". Students will learn about exponential growth and decay, and how to use the natural base "e" in real-life applications. The lesson also includes practice questions and a quiz.

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Exponential Growth and Decay with the Natural Number "e

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

  2. CA Standards: 12.0Students know the laws of fractional exponents, understand exponential functions, and use theses functions in problems involving exponential growth and decay. Objective:(1)Using The Natural Base e(2)Using e in Real Life Agenda: 02/26/15 1.) Warm-up 2.) Questions: WS Exponential Decay Practice A/B 3.) Lesson: 8.3 The Number e 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. 2.59374 2.70481 2.71692 2.71815 2.71827 2.71828 2. What value does seem to be approaching as “n” becomes larger? 2.718281828459…

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

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

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

  8. Write this 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?

  9. HOMEWORK Page 483: 4 – 80 All

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