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Section 6.2 Exponential Function Modeling and Graphs

Section 6.2 Exponential Function Modeling and Graphs. The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let N represent the number of asthma sufferers (in millions) worldwide t years after 1990.

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Section 6.2 Exponential Function Modeling and Graphs

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  1. Section 6.2Exponential Function Modeling and Graphs

  2. The number of asthma sufferers in the world was about 84 million in 1990 and 130 million in 2001. Let N represent the number of asthma sufferers (in millions) worldwide t years after 1990. • Write N as a linear function of t. What is the slope? What does it tell you about asthma sufferers? • Write N as an exponential function of t. What is the growth factor? What does it tell you about asthma sufferers? • Graph the two together. What do you notice?

  3. The half-life of a substance is the amount of time it takes for a decreasing exponential function to decay to half of its initial value • The half-life of iodine-123 is about 13 hours. You begin with 100 grams of iodine-123. • Write an equation that gives the amount of iodine remaining after t hours • Hint: You need to find your rate using the half-life information • How much iodine-123 will be left after 1 day?

  4. Doubling time is the amount of time it takes for an increasing exponential function to grow to twice its previous level • Suppose we put $1000 in the stock market 10 years ago and we now have $2000 • Write an equation for the balance B after t years • What was the annual growth rate?

  5. Consider the following table • How can we determine if this data can be represented by an exponential function? • Test for a constant ratio • Find a function for this situation • For what value of t does h(t) = 2000?

  6. In your groups graph the following exponential functions on the same screen • Use a window with -5 ≤ x ≤ 5 and 0 ≤ y ≤ 70 • What do you notice about the graphs • What are there y-intercepts? • Are they decreasing or increasing? • Are they concave up or concave down? • What are their domains and ranges?

  7. Let’s look at the following graphs • What is going on with these graphs? • What can you say about their y-intercepts? • What can you say about the rate they are increasing?

  8. Horizontal Asymptotes • All exponential functions have a horizontal asymptote • This is the place where the function “levels off” • It is at the horizontal axis (unless the exponential function has been shifted up or down) y x

  9. Let’s try a few from the chapter 6.2 – 6, 7, 14, 15, 21, 22, 33

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