Answer
(a) $549.2$ million metric tons
(b) $2019$.
Work Step by Step
(a) Given $y=0.0429x^2-9.73x+606$, for $x=2014-2008=6$, we have $y=0.0429(6)^2-9.73(6)+606\approx549.2$ million metric tons
(b) let $y=500$, we have $500=0.0429x^2-9.73x+606$ or $0.0429x^2-9.73x+106=0$ which can be solved using the quadratic formula (discard the other bigger number) to get $x\approx11$ which means year $2019$.