Section 3.2Comparing Exponential and Linear

Functions

• Given the following table:

• What type of function would be appropriate for modeling this data?– Hint: Compute the average rate of change for the

intervals or make a scatter plot

• Let’s see if we can make a function for this data– What is the range and domain of our function?

x 1 2 4 5 8 9

f(x) 4096 1024 64 16 0.25 0.0625

• 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?

• Let’s compare the growth rate of linear and exponential functions– Plot f(x) = 5x + 20 and g(x) = 3(1.08)x on the same

graph– Which is growing faster?

• In your groups do problems 19, 22, and 29