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Chapter 8-1 Exploring Exponential Models

Chapter 8-1 Exploring Exponential Models. Essential Question: How do you find a growth factor and a decay factor?. 8-1: Exploring Exponential Models. An exponential function is a function with the general form y = ab x , with the following rules: a ≠ 0 b > 0 and b ≠ 1 x is a real number

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Chapter 8-1 Exploring Exponential Models

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  1. Chapter 8-1Exploring Exponential Models Essential Question: How do you find a growth factor and a decay factor?

  2. 8-1: Exploring Exponential Models • An exponential function is a function with the general form y = abx, with the following rules: • a ≠ 0 • b > 0 and b ≠ 1 • x is a real number • When b > 1, b is called the growth factor

  3. 8-1: Exploring Exponential Models • Graphing Exponential Growth • Example: Graph y = 2x • Step 1: Make a table of values • Step 2: Graph the coordinates with a smooth curve

  4. 8-1: Exploring Exponential Models • If you know the rate of increase r, you can find the growth factor by using the equation b = 1 + r • Example: In 2000, the population was 281 million and the annual rate of increase in the US population was about 1.24%. Suppose that increase continues to be 1.24%. Which function best models US population growth, in millions, after 2000? • 281 + 1.0124x Hints: • 281(1.24)x • 281(1.024)x • 281(1.0124)x #1) Remember the form y = abx #2) What is 1.24% written as a decimal?

  5. 8-1: Exploring Exponential Models • Using the function from the previous slide • y = 281(1.0124)x • Predict the US population in 2015 to the nearest million • Suppose the rate of population increase changes to 1.4%. Write a function to model population growth and then use it to predict the 2015 population to the nearest million. 281(1.0124)15 ≈ 338 million 281(1.014)15 ≈ 346 million

  6. 8-1: Exploring Exponential Models • An exponential function is a function with the general form y = abx, with the following rules: • a ≠ 0 • b > 0 and b ≠ 1 • x is a real number • When 0 < b < 1, b is called the decay factor

  7. 8-1: Exploring Exponential Models • Without graphing, determine whether the function y = 14(0.95)x represents exponential growth or exponential decay • Your Turn: Without graphing, determine whether the following functions represent exponential growth or exponential decay • y = 100(0.12)x • y = 0.2(5)x • y = 16(½)x Since b < 1, this function represents exponential decay Exponential decay Exponential growth Exponential decay

  8. 8-1: Exploring Exponential Models • Assignment • Page 434 – 435 • Problems 1 – 9, 17 – 31 (odd problems)

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