#### Answer

(a) \$29070
(b) \$33228

#### Work Step by Step

(a) The objective is to use the formula to find the average cost per inmate in the United States in 2013 and check whether the mathematical model overestimates or underestimates the data shown by the graph.
The mathematical formula is : $C= 594n + 21348$ where n is the number of years after 2000.
For 2013, the value of n is 13 as per $n= 2013- 2000$.
Using the value of n= 13 in the formula, then
$$ C= 594n + 21348 = 594(13) + 21348 = 7733 + 21348 = 29070. $$
Thus, the average cost per inmate in the United States in 2013 obtained by the formula is \$29070.
As the amount shown by the graph is \$29291, the difference between the amount shown on the graph and the amount given by the formula is
$$ \$29291-\$29070 = \$221 $$
So, the average cost per inmate in the United States in 2013 obtained by the formula underestimates the average annual cost per inmate in the United States in 2013 by \$221.
(b) If the trend from 2000 to 2013 continues, then the objective is to project the cost per inmate in the United States in 2020.
The formula for this is $C = 594n + 21348$
For 2020, the value of n is 20 as given by $n= 2020-2000$.
Using the value of n=20 in this formula,
$$C = 594n + 21348= 594(20) + 21348 + 11880 + 21348 = 33228$$
The average annual cost per inmate in the United States in 2020 obtained by the formula is \$33228