Answer
a) Total cost = $22,128.
b) The model estimates the same cost as in part (a).
Work Step by Step
(a)
The charges of public institutions which are given for the period of four years are 5249, 5413, 5629 and 5837 dollars.
Thus, the total costs of the public dormitory charges will be:
$\$5249+\$5413+\$5629+\$5837=\$22,128$.
(b)
Using the given model we get, $\begin{align}
& {{a}_{1}}=198\left( 1 \right)+5037 \\
& {{a}_{1}}=5235 \\
& {{a}_{4}}=198\left( 4 \right)+5037 \\
& {{a}_{4}}=5829
\end{align}$
So, $\begin{align}
& {{S}_{n}}=\frac{n}{2}\left( {{a}_{1}}+{{a}_{n}} \right) \\
& {{S}_{n}}=\frac{4}{2}\left( 5235+5829 \right) \\
& {{S}_{n}}=2\left( 11,064 \right) \\
& {{S}_{n}}=\$22,128\\\end{align}$
