Question

a cell - phone plan charges $19.95 per month plus $1.25 in taxes, plus $0.10 per minute for calls beyond the 100 - minute monthly limit. write a piecewise - defined function to model the monthly cost $c(x)$ as a function of the number of minutes used for the month.

Explanation:

Step1: Define cases

Let $x$ be the number of minutes used in a month.
If $0\leq x\leq100$, the monthly cost $C(x)$ is just the fixed - monthly charge plus the tax. The fixed - monthly charge is $\$13$ and the tax is $\$1.50$. So $C(x)=13 + 1.50=14.50$.

Step2: Consider minutes over 100

If $x>100$, the cost consists of the fixed - monthly charge, the tax, and the charge for the extra minutes. The fixed - monthly charge is $\$13$, the tax is $\$1.50$, and the charge for the extra minutes is $0.60(x - 100)$. So $C(x)=13+1.50+0.60(x - 100)=14.50+0.6x-60=0.6x - 45.5$.

Answer:

$C(x)=

$$\begin{cases}14.50, &\text{if }0\leq x\leq100\\0.6x - 45.5, &\text{if }x > 100\end{cases}$$

$