Answer
The year is $ 2013 $
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) = \$23,345 $ plug into model $ 1 $
$ 23,345=442x+12,969 $
Simplify.
$ 23,345-12,969= 442x $
$ 10376 = 442x $
$ \frac{10376}{442} = x $
$ 23.48 = x $
$ 23 = x $
The year is $ = 1990+23 = 2013 $
