Answer
a) 185.312 million metric tons
b) maximum
c) 2013
d) 186.82 million metric tons
Work Step by Step
a)
$2018-2000=18$
$f(x)=-.072x^2+1.93x+173.9$
$f(18)=-.072*18^2+1.93*18+173.9$
$f(18)=-.072*324+34.74+173.9$
$f(18)=-23.328+34.74+173.9$
$f(18)=185.312$
b)
The coefficient of the $x^2$ term is negative, so the graph opens down. Since the graph opens down, the vertex of the graph is the graph’s maximum point.
c)
$f(x)=-.072x^2+1.93x+173.9$
The highest (or lowest) point on a graph is found using the vertex of a graph. The vertex of the graph has the equation $x=-b/2a$.
$a=-.072$, $b=1.93$, $c=173.9$
$x=-b/2a$
$x=-1.93/2*-.072$
$x=1.93/.144$
$x=13.4$
Rounded to the nearest number, $x=13$
$13+2000=2013$
d)
$f(x)=-.072x^2+1.93x+173.9$
$f(13)=-.072*13^2+1.93*13+173.9$
$f(13)=-.072*169+25.09+173.9$
$f(13)=-12.168+198.99$
$f(13)=186.822$
