Q. 50 - Precalculus Enhanced with Graphing Utilities

Question

Long Distance A phone company offers a domestic long distance package by charging \(5 plus \)0.05 per minute. 

(a) Write a linear model that relates the cost C, in dollars, of talking x minutes. 

(b) What is the cost of talking 105 minutes? 180 minutes? 

Step-by-Step Solution

Answer

Part (a) The function is $C\left(x\right)=0.05x+5$.

Part (b) The cost of talking 105 minutes is $10.25 and for 180 minutes is $14.

Part (a) Step 1. Given Information.

A domestic long distance package has charge $5 plus $0.05 per minute. 

Part (a) Step 2. Explanation.

Find a linear model where, the cost C, in dollars, of talking x minutes. 

A domestic long distance package has charge is fix. this is y- intercept. 

$b=5$.

A charge per minute is varying with x . This is slope $m=0.05$.

So the function becomes  $C\left(x\right)=0.05x+5$.

Part (b) Step 1. Explanation.

Find the cost of talking for 105 minutes.

We have $x=105$, Find $C\left(x\right)$.

$$\begin{gathered} C\left(x\right)=0.05x+5 \\ =0.05\left(105\right)+5 \\ =10.25 \end{gathered}$$

The cost of talking 105 minutes is $10.25.

Find the cost of talking for 180minutes.

We have$x=180$. Find C(x).

$$\begin{gathered} C\left(x\right)=0.05x+5 \\ =0.05\left(180\right)+5 \\ =14 \end{gathered}$$

The cost of talking 180 minutes is $14.