## Precalculus (6th Edition) Blitzer

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 $t>450$