Answer
(a.) model $ 1: \$ 28,845 $ Underestimates by $ \$211$
model $ 2: \$ 28,920 $ Underrestimates by $ \$136 $.
(b.) The year is 2021.
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 $ 2012 $ is
$ x=2012-2000= 12 $
Plug the value $ x=12 $ into both models.
model $ 1 : $
$ T(12)=1157(12)+14,961 $
Simplify.
$ T(12)= 28,845 $
From the graph the value $ T(12) = 29,056 $
Therefore the model 1 underestimates by $ 29,056 - 28,845 = 211 $
model $ 2 : $
$ T(12)=21(12)^2+862(12)+15,552 $
Simplify.
$ T(12)=28,920 $
From the graph the value $ T(12) = 29,056 $
Therefore the model $ 2 $ underestimates by $ 29,056 - 28,920 = 136 $
(b.) The given model $ 1 $ is
$ T(x)=1157x+14,961 $
The given value of $ T(x) $ is $ \$39,258 $ plut into the model $ 1 $.
$ 39,258=1157x+14,961 $
$ 39,258-14,961=1157x $
$ 24,297=1157x $
$ \frac{24,297}{1157}=x $
$ 21 = x $
The year is $ 2000+21 = 2021 $
