Answer
(a.) model $ 1: \$ 31,159 $ Underestimates by $ \$ 542 $
model $ 2: \$ 31,736 $ Overestimates by $ \$ 35 $.
(b.) The year is $ 2019 $.
Work Step by Step
(a.) The given two mathematical models are
model $ 1 : $ $ T=1157x+14,961 $
and
model $ 2 : $ $ T=21x^2+862x+15,552 $
Where $ T $ is average cost of tuition and fees and $ x $ is number of years after $ 2000 $.
The average cost of tuition for $ 2014 $ is
$ x=2014-2000= 14 $
Plug the value $ x=14 $ into both models.
model $ 1 : $
$ T(14)=1157(14)+14,961 $
Simplify.
$ T(14)= 31,159 $
From the graph the value $ T(14) = 31,701 $
Therefore the model 1 underestimates by $ 31,701 - 31, 159 = 542 $
model $ 2 : $
$ T(14)=21(14)^2+862(14)+15,552 $
Simplify.
$ T(14)=31,736 $
From the graph the value $ T(14) = 31,701 $
Therefore the model $ 2 $ overestimates by $ 31,736 - 31, 701 = 35 $
(b.) The given model $ 1 $ is
$ T(x)=1157x+14,961 $
The given value of $ T(x) $ is $ \$36,944 $ plug into the model $ 1 $.
$ 36,944=1157x+14,961 $
$ 36,944-14,961=1157x $
$ 22,016=1157x $
$ \frac{22,016}{1157}=x $
$ 19.0285 = x $
$ 19 = x $
The year is $ 2000+19 = 2019 $
