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Chapter 3: Problem 13

Write a variation model using \(k\) as the constant of variation. The average cost per minute \(\bar{C}\) for a flat rate cell phone plan is inversely proportional to the number of minutes used \(n\).

Short Answer

Expert verified
\(\bar{C} = \frac{k}{n}\)

Step by step solution

01

Understand Inverse Proportionality

When a value is inversely proportional to another, it means as one increases, the other decreases. Mathematically, this can be expressed as the product of the two values being equal to a constant. For this problem, it means \(\bar{C} \times n = k\).
02

Write the Variation Model

Given that \(\bar{C}\) is inversely proportional to \(n\), we can write the relationship as \(\bar{C} = \frac{k}{n}\). Here, \k\ is the constant of variation.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

inverse proportionality
Inverse proportionality describes a relationship where one quantity increases while the other decreases.
In mathematical terms, if two variables are inversely proportional, their product is always equal to a constant.
For example, if we have variables \(x\) and \(y\), and they are inversely proportional, it means \(x \times y = k\), where \(k\) is a constant.
In the context of the provided exercise, the average cost per minute \(\bar{C}\) for a flat rate cell phone plan is inversely proportional to the number of minutes used \(n\).
Hence, \(\bar{C} \times n = k\). This relationship shows that as you use more minutes (increase \(n\)), the average cost per minute \(\bar{C}\) decreases, and vice versa.
It's a fundamental concept that helps in understanding various real-world scenarios where one factor diminishes as another grows.
constant of variation
The constant of variation \(k\) is a key element in inverse proportionality.
It remains the same no matter how the values of the variables change.
In our example of the average cost per minute and the number of minutes used, \(\bar{C} \times n = k\) represents this constant relationship.
To find the constant of variation, you can multiply the values of the inversely proportional variables.
For instance, if you know that for 100 minutes (\

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Most popular questions from this chapter

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