From the data given above, we can see that we have the data starting from the year 2003.
We need to find the equation that can relate the variation of the average cost of the tuition with time.
First of all we will find the equation:
Considering 'x' axis as the time and 'y' axis as the average cost of the tuition:
Now, lets say year 2003 is the first year as per the data, we can assume the value of time as t=1 for the year 2003, t=2 for the year 2004, t=3 for the year 2005 .... and so on.
we can have two sets of the co-ordinates:
[tex](1, 15505)[/tex] and [tex](2, 16510)[/tex]
Using these two sets of co-ordinates we can find the equation of the line:
We can use slope intercept formula to find the equation of the line, using the formula:
[tex](y-y_{1})=\frac{x_{2}-x_{1}}{y_{2}-y_{1}}(x-x_{1})[/tex]
we can plug in the values to get,
[tex](y-15505)=\frac{16510-15505}{2004-2003}(x-2003)[/tex]
[tex](y-15505)=\frac{1005}{1}(x-1)[/tex]
[tex]y-15505=1005\times x-1005[/tex]
[tex]y=1005x-1005+15505=1005x+14500[/tex]
So, we get the equation of the line as
[tex]y=1005x+14500[/tex]
We need to find the average cost of tuition in the year 2000 for that we can need to use [tex]t=-3[/tex], where 't' represents time on the x-axis.
Putting [tex]t=-3[/tex] in the equation, we get:
[tex]y=1005\times (-3)+14500=-3015+14500=11485[/tex]
Therefore,
The best estimate for the average cost of tuition for the year 2000 is $11,485.
