Q. 47 - Precalculus Enhanced with Graphing Utilities

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:

$C\left(x\right)=\left\{\begin{array}{l}39.99 if 0\le x\le 450\\ 0.45x-162.51 if x>450\end{array}\right.$

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. $451$
   

Step-by-Step Solution

Answer

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

Step 1. Given Information

We are given a function, 

$C\left(x\right)=\left\{\begin{array}{l}39.99 if 0\le x\le 450\\ 0.45x-162.51 if x>450\end{array}\right.$

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 $\$40.44$