1. Section 6.2 Exponential 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? t912151821 h(t)h(t)1202163897001260

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) x y

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