Answer
The simplified algebraic expression is as follows:
\[C\left( t \right)=\left\{ \begin{align}
& 30\text{ if 0}\le t\le \text{120} \\
& 0.3t-6\text{ if }t>120 \\
\end{align} \right.\]
Work Step by Step
Consider the algebraic expression:
$C\left( t \right)=\left\{ \begin{align}
& 30,\text{ if 0}\le t\le \text{120} \\
& \text{30+0}\text{.3}\left( t-120 \right)\text{, if }t>120 \\
\end{align} \right.$
Simplify the above expression and write the simplified form as below:
$\begin{align}
& \text{30+0}\text{.3}\left( t-120 \right)=30+0.3t-36 \\
& =0.3t-6
\end{align}$
So,
$C\left( t \right)=\left\{ \begin{align}
& 30,\text{ if 0}\le t\le \text{120} \\
& 0.3t-6,\text{ if }t>120 \\
\end{align} \right.$
Hence, the simplified algebraic expression is:
$C\left( t \right)=\left\{ \begin{align}
& 30,\text{ if 0}\le t\le \text{120} \\
& 0.3t-6,\text{ if }t>120 \\
\end{align} \right.$
