Answer
The model $ 2 $ is better description and it overestimates by $ \$ 146$
Work Step by Step
The given two mathematical models are
model $ 1 : $ $ C=442x+12,969 $
and
model $ 2 : $ $ C=2x^2+390x+13,126 $
Where $ C $ is cost $ x $ years after $ 1990 $ of what cost $ \$10,000 $ in $ 1984 $.
The average cost of tuition for $ 1990 $ is
$ x=2013-1990=23 $
Plug the value $ x=23 $ into both models.
model $ 1 : $
$ C(23)=442(23)+12,969 $
Simplify.
$ C(23)= 22,862 $
From the graph the value $ C(23) = \$ 23,300 $.
Therefore the model 1 underestimates by $ 23,300 - 22,862 = 438 $
model $ 2 : $
$ C(23)=2(23)^2+390(23)+13,126 $
Simplify.
$ C(23)=23,154 $
From the graph the value $ C(0) = \$ 23,300 $.
Therefore the model $ 2 $ Underestimates by $ 23,300 - 23,154 = 146 $
