Answer
2008: $67.36\%$
2009: $70.13\%$
2010: $72.90\%$
2011: $75.67\%$
2012: $79.30\%$
2013: $81.25\%$
2014: $82.20\%$
Work Step by Step
We are given the function:
$p(t)=\begin{cases}
2.77t+45.2,8\leq t\leq 11\\
1.95t+55.9,12\leq t\leq 14
\end{cases}$
As $t=8$ corresponds to 2008, it means that $t=9$ corresponds to 2009, $t=10$ to 2010, $t=11$ to 2011, $t=12$ to 2012, $t=13$ to 2013 and $t=14$ to 2014.
Compute $p(t)$ for $t=8,9,10,11$:
2008:
$p(8)=2.77(8)+45.2=67.36$
2009:
$p(9)=2.77(9)+45.2=70.13$
2010:
$p(10)=2.77(10)+45.2=72.90$
2011:
$p(11)=2.77(11)+45.2=75.67$
Compute $p(t)$ for $t=12,13,14$:
2012:
$p(12)=1.95(12)+55.9=79.30$
2013:
$p(13)=1.95(13)+55.9=81.25$
2014:
$p(14)=1.95(14)+55.9=83.20$
