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Understanding Natural Base & Exponential Growth in Precalculus

Explore the concept of Natural Base e=2.718 in Precalculus, distinguish between exponential growth and decay functions, practice solving exponential equations, and learn about graphing transformations. Includes homework for further practice.

george-allison
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Understanding Natural Base & Exponential Growth in Precalculus

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  1. Today in Precalculus • Go over homework • Notes: Intro to Natural Base (you’ll need a calculator) • Homework

  2. Natural Base Natural Base is known as e. (e≈2.718 irrational like π) Named for Leonhard Euler y = a•ekx One of the ten basic functions If k>0, exponential growth If k<0, exponential decay

  3. Natural Base Find the value for the following functions: • y = 3e2x x = 4 y = 8942.874 • y = -5e-3x x = 2 y = -0.012

  4. Exponential Growth/Decay State if the following are exponential growth or decay functions. a) y = e2x b) y = e–2x c) y = 2–x d) y = 0.6–x Exponential Growth (k>0) Exponential Decay (k<0) Exponential Growth (b>0) but reflected across y-axis, so decay Exponential Decay (0<b<1) but reflected across y-axis, so growth

  5. Graphing y = 2ex-1 Vertical stretch 2 Shift right 1 y = e2x+1 Horizontal shrink ½ Shift up 1

  6. Homework • Page 286: 15, 17, 19, 21, 22, 24, 31-34, 57, 58

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