Answer
$f(12)=15.54$, diamond production is predicted to be worth 15.54 billion dollars in 2012.
Work Step by Step
We are given that the function $f(x)=.42x+10.5$, can be used to predict diamond production (where x is the number of years after 2000).
To predict diamond production in 2012, we must first find x.
$2012-2000=12$ years, so $x=12$.
Next, we can insert x into the function.
$f(12)=.42\times12+10.5=5.04+10.5=15.54$
Thus $f(12)=15.54$ tells us that diamond production is predicted to be worth 15.54 billion dollars in 2012.