Answer
(a) $f(x)=622.25x+22036$. See graph and explanations.
(b) $23903$ dollars.
(c) $f(x)=653x+21634$
Work Step by Step
(a) To find the linear function $f(x)=ax+b$, use the data points $(0,22036)$ and $(4,24525)$, we have $a=\frac{24525-22036}{4-0}=622.25$. Use the first point, we have $b=22036$, thus we have $f(x)=622.25x+22036$. See graph. The slope of the graph indicates the average increase of tuition fees per year from 2009 to 2013.
(b) For year 2012, we have $x=2012-2009=3$ and $f(3)=622.25(3)+22036=23902.75\approx23903$ dollars.
Compare to the actual value of $23460$, the prediction is close.
(c) Use the linear regression feature of a graphing calculator, we can find the equation of the line of best fit as $f(x)=653x+21634$