Answer
The simplified algebraic expression is\[C\left( t \right)=\left\{ \begin{align}
& 40\text{ if 0}\le t\le \text{200} \\
& 0.3t-20\text{ if }t>200 \\
\end{align} \right.\].
Work Step by Step
Consider the expression for the cost:
$C\left( t \right)=\left\{ \begin{align}
& 40\text{ if 0}\le t\le \text{200} \\
& \text{40+0}\text{.3}\left( t-200 \right)\text{ if }t>200 \\
\end{align} \right.$
We will solve the second part of the piecewise function as follows:
$\begin{align}
& 40+0.3\left( t-200 \right)=40+0.3t-0.3\times 200 \\
& =40+0.3t-60 \\
& =0.3t-20
\end{align}$
Now, write the simplified form of the expression for the cost as follows:
$C\left( t \right)=\left\{ \begin{align}
& 40\text{ if 0}\le t\le \text{200} \\
& 0.3t-20\text{ if }t>200 \\
\end{align} \right.$
Hence, the simplified expression for the cost is $C\left( t \right)=\left\{ \begin{align}
& 40\text{ if 0}\le t\le \text{200} \\
& 0.3t-20\text{ if }t>200 \\
\end{align} \right.$.
