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)

1994 11,719

 1996 13,994

 1998 17,709

2000 16,233

 2002 21,116

2004 24,101

2006 32,218 

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. 

  Function 1: 

 Function 2: 

 Function 3:

 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. 

  Function 1: 

 Function 2: 

  Function 3: 

 Function of choice: 

 Explanation: