Q. 38 - Precalculus Enhanced with Graphing Utilities

Question

Phone Charges The monthly cost C, in dollars, for international calls on a certain cellular phone plan is modeled by the function $C\left(x\right)=0.38x+5$, where x is the number of minutes used.

 (a) What is the cost if you talk on the phone for$x = 50$ minutes?

 (b) Suppose that your monthly bill is \(29.32. How many minutes did you use the phone? 

(c) Suppose that you budget yourself \)60 per month for the phone. What is the maximum number of minutes that you can talk? 

(d) What is the implied domain of C if there are 30 days in the month? 

(e) Interpret the slope. 

( f) Interpret the y-intercept. 

Step-by-Step Solution

Answer

Part (a) The cost of phone for 50 minutes is $24.

Part (b) The phone used for 64 minutes for a monthly bill of $29.32.

Part (c)  For the budget of $60per month for the phone, maximum 144 minutes can talk.

Part (d) The implied domain of C will be $\left\{x|0\le x\le 43200\right\}$.

Part (e) The slope is $m=0.38$ and it represents the charge of phone is 0.38 per minute.

Part (f) y- intercept is $b=5$ and it represent monthly rent for phone bill.

Part (a) Step 1. Given information.

The monthly cost C, for international calls on a certain cellular phone plan is modeled by the function $C\left(x\right)=0.38x+5$, where x is the number of minutes used 

Part (a) Step 2. Explanation.

Find the cost of talk on the phone for $x=50$ minutes.

Substitute $x=50$ in $C\left(x\right)=0.38x+5$.

$$\begin{gathered} C\left(x\right)=0.38x+5 \\ =0.38\left(50\right)+5 \\ =24 \end{gathered}$$

The cost is $24.

Part (b) Step 1. Explanation.

Find how many minutes the phone did use, if the monthly bill is $29.32.

We have $C\left(x\right)=29.32$ find x.

$$\begin{gathered} C\left(x\right)=29.32 \\ 0.38x+5=29.32 \\ 0.38x=24.32 \\ x=64 \end{gathered}$$

The phone used for 64 minutes for a month.

Part (c) Step 1. Explanation.

The monthly budget for the phone is $60. So $C\left(x\right)\le 60$.

Find the maximum number of minutes can talk.

$$\begin{gathered} C\left(x\right)\le 60 \\ 0.38x+5\le 60 \\ 0.38x\le 55 \\ x\le 144.74 \end{gathered}$$

Maximum 144 minutes can talk.

Part (d) Step 1. Explanation.

Find the implied domain of C , for 30 days in the month.

In a month of 30 days, there are $60\times 24\times 30=43200$ minutes.

There will be minimum 0 minutes and maximum 43200 minutes in a month. 

So, the implied domain of C will be $\left\{x|0\le x\le 43200\right\}$

Part (e) Step 1. Explanation.

Interpret the slope.

Compare modeled by the function $C\left(x\right)=0.38x+5$ with standard linear function $y=mx+b$, here m is slope and b is y- intercept.

So, we have $m=0.38$.

Slope is average rate of change. so, here slope represent the charge of phone is 0.38 per minute.

Part (f) Step 1. Explanation.

Interpret the y-intercept.

Compare modeled by the function $C\left(x\right)=0.38x+5$  with standard linear function $y=mx+b$ 

here m is slope and b is y- intercept.

So, we have $b=5$.

y- intercept is point at which graph intercept y-axis. here it represent monthly rent for phone bill.