Question

write a piece - wise function that models the cellular phone billing plan described below. let x represent the number of minutes used and c(x) represent the cost for those x minutes. then graph the function. $25.00 per month buys 350 minutes. additional time costs $0.20 per minute. fill in the missing values or expressions for the piece - wise function below. c(x)=\begin{cases}square&\text{if }0leq x<square\square&\text{if }squareleq xend{cases} (simplify your answer. do not include the $ symbol in your answer.)

Explanation:

Step1: Analyze the first - part of the plan

For $0\leq x\leq350$, the cost is a flat - rate of $25$. So, when $0\leq x\leq350$, $C(x) = 25$.

Step2: Analyze the second - part of the plan

For $x>350$, the cost is the initial $25$ plus $0.20$ for each minute over $350$. The number of minutes over $350$ is $x - 350$. So the cost function is $C(x)=25+0.20(x - 350)=25 + 0.2x-70=0.2x - 45$.

Answer:

$C(x)=

$$\begin{cases}25& \text{if }0\leq x\leq350\\0.2x - 45& \text{if }x>350\end{cases}$$

$