Question

Cell Phone Service Sprint PCS offers a monthly cellular phone plan for $\backslash (39.99$. It includes $450$anytime minutes and charges $\backslash )0.45$per minute for additional minutes. The following function is used to compute the monthly cost for a subscriber:

$C\left(x\right)=\left\{\begin{array}{l}39.99if0\le x\le 450\\ 0.45x-162.51ifx>450\end{array}\right.$

where x is the number of anytime minutes used. Compute the monthly cost of the cellular phone for use of the following number of anytime minutes:

1. $200$
   
2. $465$
   
3. $451$
   

Short answer

1. The monthly cost is $\$39.99$.
2. The monthly cost is $\$46.74$.
3. The monthly cost is $\$40.44$.

Step-by-step solution

Step 1. Given Information 

We are given a function,

$C\left(x\right)=\left\{\begin{array}{l}39.99if0\le x\le 450\\ 0.45x-162.51ifx>450\end{array}\right.$

Part(a) Step 1. Finding part(a) 

For $x=200$, the given function is equal to $39.99$

$C\left(200\right)=39.99$

Hence the monthly cost is$\$39.99$

Part(b) Step 1. Finding part(b) 

Since $465>450$, so the function will be,

$C\left(x\right)=0.45x-162.51$

Putting $x=465$in the function, we get

$$\begin{gathered} C\left(465\right)=0.45\left(465\right)-162.51 \\ C\left(465\right)=209.25-162.51 \\ C\left(465\right)=46.74 \end{gathered}$$

Hence the monthly cost is$\$46.74$

Part(c) Step 1. Finding part(c)  

Putting $x=451$in the given function, we get

$$\begin{gathered} C\left(451\right)=0.45\left(451\right)-162.51 \\ C\left(451\right)=202.95-162.51 \\ C\left(451\right)=40.44 \end{gathered}$$

Hence the monthly cost is$\$40.44$