Question

a cell - phone plan charges $40.85 per month plus $13.94 in taxes, plus $0.60 per minute for calls beyond the 300 - minute monthly limit. write a piece - wise defined function to model the monthly cost c(x) (in $) as a function of the number of minutes used for the month.
c(x) = { 54.79 for 0 <= x <= 300
{ 54.79+0.6(x - 300) for x>300

Explanation:

Step1: Calculate cost for $0\leq x\leq300$

The monthly charge is $40.25$ and taxes are $13.94$. So the total cost $C(x)$ for $0\leq x\leq300$ is $40.25 + 13.94=54.19$.

Step2: Calculate cost for $x > 300$

The base - cost (for $0\leq x\leq300$) is $54.19$. The number of minutes over 300 is $x - 300$. The cost per minute over 300 is $0.60$. So the cost function for $x>300$ is $C(x)=54.19+0.60(x - 300)=54.19+0.6x-180=0.6x - 125.81$.

Answer:

$C(x)=

$$\begin{cases}54.19&\text{for }0\leq x\leq300\\0.6x - 125.81&\text{for }x > 300\end{cases}$$

$