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Graphs of Exponential Functions

Explore the impact of 'a' and 'b' in exponential functions through graphing and analysis. Learn how these parameters affect the steepness and position of the graphs. Practice graphing variations and verify conclusions using spreadsheets. Understand horizontal asymptotes and restrictions on 'b'. Apply the concepts to real-world scenarios like sales revenue modeling.

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Graphs of Exponential Functions

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  1. Graphs of Exponential Functions Lesson 3.3

  2. How Does a*bt Work? • Given f(t) = a * bt • What effect does the a have? • What effect does the b have? • Try graphing the following on the same axes3 * 1.1X 0.75 * 1.1X2 * 1.1X 0.5 * 1.1X1.5 * 1.1X Set the window at -5<x<5-10<y<10

  3. How Does a*bt Work? • Conclusion • All the graphs cross the y-axis at A • The graph is steeper for some x

  4. How Does a*btWork? • Now let’s try to see what happens when we change the value for b • Specify the following in the Y= screen2*1.1x 2*1.5x 2*2.0x 2*2.5x Verify conclusions with spreadsheet from previous lesson. Set the window at -5<x<5-10<y<10

  5. How Does a*btWork? • Results: • All graphs cross the y-axis at y=2 • If b is low: high to left, shallow up to right • If b is large: low to the left, steeper sooner on the right

  6. How Does a*bt Work? • Consider 0 < b < 1 • Graph the following:2*0.75x 2*0.5x 2*0.25x 2*0.1x Set the window at -5<x<5-10<y<10

  7. How Does a*btWork? • Results when 0 < b < 1 • Graph is up to the left, down to the right

  8. Assignment A • Lesson 3.3A • Page 127 • Exercises 1 – 25 odd

  9. Horizontal Asymptotes • When b > 1, f(x) 0 as x  -∞ • When 0 < b < 1, f(x) 0 as x +∞ View Nspire demo

  10. Restrictions on b • Note always b > 0 … cannot have • Fractional power of b when b < 0 • It is not a continuous function • Also note that calculator will do some funny things with y = (-2)^x ???

  11. Sales of Compaq • Revenue from Compaq Computers • Use your calculators to determine an exponential regression modeling function

  12. Assignment • Lesson 3.3B • Page 128 • Exercises 27 – 41 odd

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