#### Answer

$a.\quad U=10n+137$
$b.\quad $257 million, exact value

#### Work Step by Step

a.
$ U=4(2n+32)+2(n+\displaystyle \frac{9}{2})\qquad$... distribute
$ U=(8n+128)+(2n+9)\qquad$... get rid of parentheses
$ U=8n+128+2n+9\qquad$...rearrange and group like terms
$U=(8n+2n)+(128+9)$
$U=10n+137$
b.
In 2012 (12 years after 2000), $n=12$. Substituting,
$U=10(12)+137$
$=120+137$
$=257$ (million)
The same value is shown on the graph, so the model gives the exact value for 2012.