Answer
$165.722; 182.787; 198.288; 212.275; 224.748$
$218.371; 194.056; 177.499; 168.700; 167.659$
$177.256;197.321;209.044$
Work Step by Step
We are given the function:
$p(t)=\begin{cases}
-0.757t^2+20.80t+127.2,2\leq t\leq 6\\
3.879t^2-82.50t+605.8,7\leq t\leq 11\\
-4.171t^2+124.34t-714.2,12\leq t\leq 14
\end{cases}$
Compute $p(t)$ for $t=2,3,4,5,6$:
2002:
$p(2)=-0.757(2^2)+20.80(2)+127.2=165.722$
2003:
$p(3)=-0.757(3^2)+20.80(3)+127.2=182.787$
2004:
$p(4)=-0.757(4^2)+20.80(4)+127.2=198.288$
2005:
$p(5)=-0.757(5^2)+20.80(5)+127.2=212.275$
2006:
$p(6)=-0.757(6^2)+20.80(6)+127.2=224.748$
Compute $p(t)$ for $t=7,8,9,10,11$:
2007:
$p(7)=3.879(7^2)-82.50(7)+605.8=218.371$
2007:
$p(7)=3.879(7^2)-82.50(7)+605.8=218.371$
2008:
$p(8)=3.879(8^2)-82.50(8)+605.8=194.056$
2009:
$p(9)=3.879(9^2)-82.50(9)+605.8=177.499$
2010:
$p(10)=3.879(10^2)-82.50(10)+605.8=168.700$
2011:
$p(11)=3.879(11^2)-82.50(11)+605.8=167.659$
Compute $p(t)$ for $t=12,13,14$:
2012:
$p(12)=-4.171(12^2)+124.34(12)-714.2=177.256$
2013:
$p(13)=-4.171(13^2)+124.34(13)-714.2=197.321$
2014:
$p(14)=-4.171(14^2)+124.34(14)-714.2=209.044$
