Section 6.2Exponential 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.–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?

• 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?

• 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?

• 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?

t 9 12 15 18 21

h(t) 120 216 389 700 1260

• 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?

( ) 20(1.2) ( ) 20(0.6)

( ) 20(1.4) ( ) 20(0.8)

t t

t t

f t h t

g t k t

• 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?

tt

tt

tktg

thtf

)5.1(150)()5.1(20)(

)5.1(100)()5.1(2)(

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

• Let’s try a few from the chapter

6.2 – 6, 7, 14, 15, 21, 22, 33