Chapter 3.1, Problem 38AYU

(a)

To determine

To find: the cost of talking $50\text{ minutes}$ on the phone

Answer to Problem 38AYU

the cost of talking $50\text{ minutes}$ on the phonewill be $24.

Explanation of Solution

Given:

  $C\left(x\right)=0.38x+5$

  $x=50\text{ minutes}$

Calculation:

Replace x with 50 in the given function.

  $C\left(50\right)=0.38\left(50\right)+5$

Simplify.

  $\begin{array}{l}C\left(50\right)\text{=}19+5\\ \text{ = 24}\end{array}$

Conclusion:

Therefore, the cost of talking $50\text{ minutes}$ on the phonewill be $24.

(b)

To determine

To find: the value of x for which the value of $C\left(x\right)$ is 29.32.

Answer to Problem 38AYU

The phone was used for 64 minutes.

Explanation of Solution

Calculation:

The objective is to find the value of x for which the value of $C\left(x\right)$ is 29.32.

  $29.32=0.38x+5$

Subtract 5 from both the sides.

  $\begin{array}{l}29.32-5\text{ =}0.38x+5-5\hfill \\ 24.32=0.38x\hfill \end{array}$

Divide each side by 0.38 to isolate x .

  $\begin{array}{l}\frac{24.32}{0.38}=\frac{0.38x}{0.38}\\ \Rightarrow 64=x\end{array}$

The phone was used for 64 minutes.

Conclusion:

Therefore, the phone was used for 64 minutes.

(c)

To determine

To find: The number of minutes x for which the bill amount is $60

Answer to Problem 38AYU

The number of minutes x for which the bill amount is $60 will be about 145.

Explanation of Solution

Calculation:

The number of minutes x for which the bill amount is $60 has to be determined.

  $60=0.38x+5$

Solve for x .

  $\begin{array}{l}60-5=0.38x+5-5\\ 55=0.38x\\ 145\approx x\end{array}$

The number of minutes x for which the bill amount is $60 will be about 145.

Conclusion:

Therefore, The number of minutes x for which the bill amount is $60 will be about 145.

(d)

To determine

To describe: the implied domain of Cif there are 30 days in the month.

Answer to Problem 38AYU

The implied domain of C is $\text{Domain : }\left[0,30\right]$ .

Explanation of Solution

Calculation:

  $\begin{array}{l}C\left(x\right)=0.38x+5\\ \text{Domain : }\left[0,30\right]\end{array}$

Conclusion:

Therefore, the implied domain of C is $\text{Domain : }\left[0,30\right]$ .