Answer
See below:
Work Step by Step
Since the telephone billing plan is $\$60$ per month buys 450 minutes and the additional time costs $\$0.35$ per minute.
So, the piecewise model function for telephone billing plan can be written as below:
$C\left( t \right)=\left\{ \begin{align}
& 60\text{ if 0}\le t\le 45\text{0} \\
& \text{60+0}\text{.35}\left( t-450 \right)\text{ if }t>450 \\
\end{align} \right.$
Solve the expression $\text{60+0}\text{.35}\left( t-450 \right)$ and write the expression in the simplified form as below:
$\begin{align}
& \text{60+0}\text{.35}\left( t-450 \right)=60+0.35t-0.35\times 450 \\
& =60+0.35t-157.5 \\
& =0.35t-97.5
\end{align}$
Thus, the simplified form of the expression for the telephone billing is as below:
$C\left( t \right)=\left\{ \begin{align}
& 60\text{ if 0}\le t\le 45\text{0} \\
& 0.35t-97.5\text{ if }t>450 \\
\end{align} \right.$
The function shown above consists of 2 straight lines.
So the function can be written as $y=60$ for $0\le t\le 450$ and $y=0.35t-97.5$ for $t>450$
