Answer
$s(t)=-10t^{2}+40t+1300$
${{\$}} 1330\quad $(billion)
Work Step by Step
Since $v(t)$ is the derivative of $s(t)$= percentage at time t,
$s(t)=\displaystyle \int(-20t+40)dt$
$=-20\displaystyle \cdot\frac{t^{2}}{2}+40t+D$
$=-10t^{2}+40t+D$
Given that at $t=0,$ outstanding debt was about ${{\$}} 1300$ billion, we have:
$\quad s(0)=1300$
and, we find D: $\left[\begin{array}{l}
1300=0+0+D\\
D=1300
\end{array}\right]$
Thus,
$s(t)=-10t^{2}+40t+1300$
Evaluating at the start of 2009 $(t=1)$
$s(1)=-10(1)+40(1)+1300={{\$}} 1330\quad $(billion)
