Answer
The year is $ 2020 $
Work Step by Step
The given mathematical models is
model $ 1 : $ $ C=442x+12,969 $
Where $ C $ is cost $ x $ years after $ 1990 $ of what cost $ \$10,000 $ in $ 1984 $.
Given cost $ C(x) = \$26,229 $ plug into model $ 1 $
$ 26,229=442x+12,969 $
Simplify.
$ 26,229-12,969= 442x $
$ 13533 = 442x $
$ \frac{13533}{442} = x $
$ 30.62 = x $
$ 31 = x $
The year is $ = 1990+31 = 2020 $
