## Precalculus (6th Edition) Blitzer

Since the telephone billing plan is $\$50$per month that buys 400 minutes and the additional time costs$\$0.3$ per minute. So, we will write the piecewise model function for the telephone billing plan as follows: C\left( t \right)=\left\{ \begin{align} & 50\text{ if 0}\le t\le 4\text{00} \\ & \text{50+0}\text{.3}\left( t-400 \right)\text{ if }t>400 \\ \end{align} \right. Solve the expression $\text{50+0}\text{.3}\left( t-400 \right)$ and write the expression in the simplified form as below: \begin{align} & \text{50+0}\text{.3}\left( t-400 \right)=50+0.3t-0.3\times 400 \\ & =50+0.3t-120 \\ & =0.3t-70 \end{align} Thus, the simplified form of the expression for the telephone billing plan is as below: C\left( t \right)=\left\{ \begin{align} & 50\text{ if 0}\le t\le 4\text{00} \\ & 0.3t-70\text{ if }t>400 \\ \end{align} \right. The function shown above consists of 2 straight lines. So the function can be written as $y=50$ for $0\le t\le 400$ and $y=0.3t-70$ for $t>400$ Now the line $y=50$ is a line parallel to the x axis and at a distance 50 units above the x axis. The line $y=0.3t-70$ is a line with slope 0.3 and y intercept $-70$.