Answer
$s(t)=-0.2t^{2}+t+13$
$13.8\quad $(percentage points)
Work Step by Step
Since $v(t)$ is the derivative of $s(t)$= percentage at time t,
$s(t)=\displaystyle \int(-0.4t+1)dt$
$=-0.4\displaystyle \cdot\frac{t^{2}}{2}+t+D$
$=-0.2t^{2}+t+D$
Given that at $t=0,$ the percent of mortgages that were subprime was about $ 13\%$, we have:
$\quad s(0)=13$
and, we find D: $\left[\begin{array}{l}
13=0+0+D\\
D=13
\end{array}\right]$
Thus,
$s(t)=-0.2t^{2}+t+13$
Evaluating at the start of 2008 $(t=1)$
$s(1)=-0.2+1+13=13.8\quad $(percentage points)
