The table lists the average annual cost of tuition and fees
at private 4-year colleges for selected years.
Year Tuition and Fees (in dollars)
1. Given any two
data points with each consisting of the year and its corresponding tuition and
fees, describe in detail how you would find a linear function that models the
data shown in the table. Be sure to clearly define and interpret all components
involved in your model.
2. Determine a
linear function that models the data, where 0 x= represents 1994, and 1 x=
represents 1995, and so on. Use the points ( ) 0,11719 and( ) 12,32218 . Choose
two more combinations of points and use them to create two additional linear
functions that model the data. Record the three linear functions below.
3. How would you go about using these functions
to predict the average annual cost of tuition and fees for a future year?
Suppose you are in the marketing department for a college and you are trying to
determine which function to use to encourage future students attend your
college. Explore and state the messages that can be sent to prospective
students by each function.
4. Use all three functions to approximate
tuition and fees in 2035. State your results below. Next, choose the function
you would use to encourage prospective students and explain the reasoning
behind your choice.