Question
*5. A calling card charges \( 50 c \) for each call placed plus 3 e per minute on the call. a. Make a table that lists possible durations of phone calls and the corresponding charges. b. Write an equation for the function. c. Is the function an example of direct variation? Why or why not?
Ask by Lindsey Cox. in the United States
Mar 10,2025
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Answer
**a. Table of Phone Call Durations and Charges**
| Minutes (\( x \)) | Charge \( C(x)=50+3x \) (in cents) |
|-------------------|--------------------------------------|
| 1 | 53 |
| 2 | 56 |
| 3 | 59 |
| 4 | 62 |
| 5 | 65 |
**b. Equation for the Function**
\[
C(x)=50+3x
\]
**c. Is the Function an Example of Direct Variation?**
No, the function is not an example of direct variation because it includes a fixed fee of 50 cents, which means it doesn't pass through the origin (0,0).
Solution
**a. Table of Phone Call Duration vs. Charges**
Let \( x \) be the number of minutes of the call and \( C(x) \) be the total charge in cents. The calling card charges a fixed fee of \( 50 \) cents for each call plus \( 3 \) cents for every minute of the call. This gives the calculation:
\[
C(x)=50+3x
\]
Below is a sample table showing a few durations and their corresponding charges:
| Minutes (\( x \)) | Charge \( C(x)=50+3x \) (in cents) |
|-------------------|--------------------------------------|
| 1 | \( 50+3(1)=53 \) |
| 2 | \( 50+3(2)=56 \) |
| 3 | \( 50+3(3)=59 \) |
| 4 | \( 50+3(4)=62 \) |
| 5 | \( 50+3(5)=65 \) |
**b. Equation for the Function**
The equation that represents the charge for a phone call of duration \( x \) minutes is:
\[
C(x)=50+3x
\]
**c. Is the Function an Example of Direct Variation?**
A function is an example of direct variation if it can be written in the form:
\[
y = kx
\]
where \( k \) is a constant and there is no additional constant term. In our function \( C(x)=50+3x \), there is a fixed fee of \( 50 \) cents. This means that when \( x=0 \), \( C(0)=50 \) instead of \( 0 \).
Thus, the function is **not** an example of direct variation because of the constant term \( 50 \).
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Simplify this solution Bonus Knowledge
To help you with the calling card costs, here’s a fun perspective on creating your table and equations. For your table, you can list durations like 1 minute, 2 minutes, 5 minutes, and so forth. For example, a 1-minute call will cost 50 cents + (3 e * 1) = 53 e; a 2-minute call will be 50 cents + (3 e * 2) = 56 e. For the equation, you can express the cost \( C \) as: \( C = 50 + 3m \), where \( m \) is the duration in minutes. As for direct variation, this function does not exhibit direct variation because direct variation implies that the relationship can be represented as \( y = kx \). Here, there is a fixed charge (50 cents) added, which breaks that direct proportionality!
