Answer
a) 18,240 thousand students
b) 2010
Work Step by Step
a)
$2008-2000=8$
$f(x)=-30x^2+600x+15360$
$f(8)=-30*8^2+600*8+15360$
$f(8)=-30*64+4800+15360$
$f(8)=-1920+20160$
$f(8)=18240$
b)
$f(x)=t$
$18360=-30x^2+600x+15360$
$0=-30x^2+600x-3000$
$0/-30=(-30x^2+600x-3000)/-30$
$0=x^2-20x+100$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-(-20)±\sqrt {(-20)^2-4*1*100})/2*1$
$x=(20±\sqrt {400-4*1*100})/2$
$x=(20±\sqrt {400-400})/2$
$x=(20±\sqrt 0)/2$
$x=20/2$
$x=10$
