Chapter 3.1, Problem 38AYU

Phone Charges The monthly cost $C$, in dollars, for calls from the United States to Japan on a certain phone plan is modeled by the function $C\left(x\right)=0.24x+5$, 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 $\$20.36$. How many minutes did you use the phone?

c. Suppose that you budget yourself $\$40$ 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 $y\text{-intercept}$.

To determine

a. What is the cost if you talk for $x=50$ minutes?

b. If the monthly bill is $\$20.36$, how many minutes did you use the phone?

c. Suppose that your monthly budget for the phone is not more than $\$40$. 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 a month?

e. Interpret the slope.

f. Interpret the $y\text{-intercept}$.

Answer to Problem 38AYU

Solution:

a. $C(40)=59$

b. We drove 180 miles.

c. We can drive a maximum 300 miles.

d. $[0,\infty )$

e. The function is an increasing function.

f. $\$45$ dollars is the minimum amount to be paid for the car. 

Explanation of Solution

Given:

It is given that the cost of one day car rental is $C(x)=0.35x+45$, where $x$ is the number of miles driven.

Calculation:

a.

When $x=40$, we get

$C(40)=0.35(40)+45=59$

Therefore, we get $C(40)=59$.

b.

When $C=108$, we get

$108=0.35x+45$

$\Rightarrow 0.35x=108-45$

$\Rightarrow x=\frac{ 63}{ 0.35}=180$

Therefore, we drove 180 miles.

c.

When $C(x)\le 150$, we get

$0.35x+45\le 150$

$\Rightarrow x\le \frac{ 150-45}{ 0.35}$

$\Rightarrow x\le 300$

Therefore, we can drive a maximum 300 miles.

d.

We can see that the value of $x$ can be any number 0 and infinity.

Therefore, the domain of $C$ is $[0,\infty )$.

e.

Since, the slope is positive, we can say that the function is an increasing function.

f.

The $y\text{-intercept}$ is the value of the function when $x=0$. That is, the $y\text{-intercept}$ is the value of the car rental that we have to pay anyways. Therefore, $\$45$ dollars is the minimum amount to be paid for the car.