Answer
$W(h)=\begin{cases}
16h,0\lt h\leq 40\\
24(h-40)+640,h\gt 40
\end{cases}$
Work Step by Step
We are given the function for a regular week of 40 hours:
$W(h)=\begin{cases}
14h,0\lt h\leq 40\\
21(h-40)+560,h\gt 40
\end{cases}$
When the hourly payment increases to 16, the payment for overtime will be $(1.5(16)$, so the new function will be:
$W(h)=\begin{cases}
16h,0\lt h\leq 40\\
(1.5(16))(h-40)+40(16),h\gt 40
\end{cases}$
$W(h)=\begin{cases}
16h,0\lt h\leq 40\\
24(h-40)+640,h\gt 40
\end{cases}$
