Answer
2012
Work Step by Step
We know that the number of barrels is modeled by:
$y=-10x^2+193x+8464$
Where x is in years and y is in thousands of barrels per day. We find where the value is 9325 barrels per day:
$9325=-10x^2+193x+8464$
$0=-10x^2+193x-861$
We use the quadratic formula
$$x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$
Where b is the coefficient of the term with a variable raised to the first power, a is the coefficient of the squared term, and c is the coefficient of the term without a variable in front of it.
This gives:
x=7, 12
For this problem, we were asked to consider only the years after 2008. Given this, we see that 12 is the correct answer.
