Answer
$ H(t)=4.5t^{2}+100t+1300\quad$ (billion dollars)
Work Step by Step
$H(t)=\displaystyle \int(9t+100)dt$
$=\displaystyle \frac{9}{2}t^{2}+100t+C$
$=4.5t^{2}+100t+C$
To find C, use the given information: $H(0)=1300$
$1300=0+0+C$
$C=1300$
Thus,
$ H(t)=4.5t^{2}+100t+1300\quad$ (billion dollars)
