# The following table shows the average yearly tuition and required fees, in thousand ofdollars, charged by a certain private

Modeling data distributions

The following table shows the average yearly tuition and required fees, in thousand of dollars, charged by a certain private university in the school year beginning in the given year.
$$\begin{array}{|c|c|}\hline \text{Year} & \text{Average tuition} \\ \hline 2005 & 17.6 \\ \hline 2007 & 18.1 \\ \hline 2009 & 19.5 \\ \hline 2011 & 20.7 \\ \hline 2013 & 21.8 \\ \hline \end{array}$$
What prediction does the formula modeling this data give for average yearly tuition and required fees for the university for the academic year beginning in 2019?

2021-01-26
Let the starting year be 2000. So, the table will be,
$$\begin{array}{|c|c|} \hline x & y\\ \hline 5 & 17.6\\ \hline7 & 18.1\\\hline 9 & 19.5\\ \hline 11 & 20.7\\ \hline 13 & 21.8\\ \hline \end{array}$$
Substitute the values of a and b to find the equation.
$$\displaystyle{y}={0.55}{x}+{14.59}$$
Substitute x as 19 to find the average yearly tution in 2019.
$$\displaystyle{y}={0.55}{\left({19}\right)}+{14.59}$$
$$\displaystyle={10.45}+{14.59}$$
$$\displaystyle={25.04}$$
Multiply by 1000 to represent the required fees.
$$\displaystyle{25.04}\times{1000}=\{25},{040}$$