Question

The chart shows the cost of tuition at a certain state university. Model the data in the chart with a linear function, using the points (1,9941) and (3,11242). Predict the cost of college tuition in 2007-2008.
What is the linear model for the data?
Y=?

Answer 1

Answer:

The cost in 2007 - 2008  =  $15,795.5

The linear model for the data is y = $650.5·x + $9290.5

Step-by-step explanation:

The given data can be presented as follows;

College year,                         x,                 Estimated tuition, y

1997-1998,                             0,                 $9412

1998-1999,                             1,                  $9941

1999-2000,                            2,                 $10561

2000-2001,                            3,                 $11242

2001-2002,                            4,                  $11965

2002-2003,                            5,                  

2003-2004,                            6,                  

2004-2005,                            7,                

2005-2006,                            8,                

2006-2007,                            9,                  

2007-2008,                            10,                  

With points (1, 9941) and (3, 11242), we have the slope given by the equation;

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$

Which gives;

$m = \dfrac{11242 - 9941}{3 - 1}= 650.5$

Therefore;

y - 11242 = 650.5 × (x - 3)

y= 650.5·x - 650.5 ×3 + 11242

y = 650.5·x + 9290.5

Therefore from the above table at 2007 - 2008, the value of x should be 10, we therefore have;

y = 650.5×10 + 9290.5 = $15,795.5

The cost (estimated tuition) in 2007 - 2008  =  $15,795.5

The linear model for the data is y = 650.5·x + 9290.5.