Question 1120789: 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:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! I would use x for year after 1994 (just to make the numbers go from 0 upward) and y for the tuition
For 2006 and 32218 (12, 32218) and 1994 (0, 11719)
change in y would be 32218-11719 or 20,499
change in x is 12
slope is 1708.25
use point slope formula y-y1=m(x-x1) m slope and (x1, y1) a point
1994 is easier because x=0
y-11719=1708.25(x-0)
y=1708.25x+11719
This is probably the best pair to choose, because it encompasses the ends of the data. But any two points could be used to compare different linear models, and they would be done the same way.
One could say to prospective students for a given year x (say 2007) that the tuition would be about 11,700 (or 12,000) plus 13*1700. Or, more simply for 2007, it would be about 1700 more than 2006 and so forth. For 2010, 4 years after 2006 and 4*1708.25 is not far from 7000, one could add 7000 to the 2006 value.
For 2035, where x=41
y=1708.25*41+11719
This is $81757.25, and $80,000 would be an approximation to be given. That assumes a great many things, most of which are not likely to happen.
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