Determining the Cost Function

Oct 13, 2025 by miodeya.com 27 views

Introduction

In this article, we will explore the concept of a cost function and how it can be used to find the total cost of buying a certain number of items, in this case, bracelet charms. We will analyze the given information and determine the appropriate function to represent the total cost.

Given Information

Jharna paid $\$13.92$ for 6 bracelet charms. Each bracelet charm cost the same amount.

Determining the Cost Function

To find the total cost in dollars, $y$ , for buying $x$ bracelet charms, we need to determine the cost of one bracelet charm and then multiply it by the number of charms. Let's denote the cost of one charm as $c$ . Since Jharna paid $\$13.92$ for 6 charms, we can set up the equation:

6c = 13.92

To find the cost of one charm, we can divide both sides of the equation by 6:

c = \frac{13.92}{6}

Now that we know the cost of one charm, we can find the total cost for buying $x$ charms by multiplying the cost of one charm by the number of charms:

y = cx

Substituting the value of $c$ , we get:

y = \left(\frac{13.92}{6}\right)x

Simplifying the expression, we get:

y = 2.32x

Conclusion

Based on the given information, the function that can be used to find the total cost in dollars, $y$ , for buying $x$ bracelet charms is:

y = 2.32x

This function represents a linear relationship between the number of charms and the total cost.

Comparison of Options

Let's compare the derived function with the given options:

A. $y = 13.92x$

B. $y = 2.32x$

The correct function is option B, $y = 2.32x$ , which represents the total cost in dollars for buying $x$ bracelet charms.

Real-World Applications

The concept of a cost function has numerous real-world applications, such as:

Business: Companies use cost functions to determine the total cost of producing a certain number of products.
Economics: Economists use cost functions to analyze the relationship between the quantity of a good or service and its cost.
Finance: Financial analysts use cost functions to determine the total cost of investing in a particular asset.

Conclusion

Introduction

In our previous article, we explored the concept of a cost function and how it can be used to find the total cost of buying a certain number of items, in this case, bracelet charms. We determined the function that can be used to find the total cost in dollars, $y$ , for buying $x$ bracelet charms. In this article, we will answer some frequently asked questions related to the cost function.

Q: What is the cost function?

A: The cost function is a mathematical representation of the total cost of buying a certain number of items. In this case, the cost function is $y = 2.32x$ , where $y$ is the total cost in dollars and $x$ is the number of bracelet charms.

Q: How do I use the cost function to find the total cost?

A: To use the cost function, simply multiply the number of bracelet charms by the cost of one charm. For example, if you want to buy 10 bracelet charms, you would multiply 10 by the cost of one charm, which is $2.32.

Q: What if I want to buy a fraction of a charm? Can I still use the cost function?

A: Yes, you can still use the cost function to find the total cost, even if you want to buy a fraction of a charm. For example, if you want to buy 0.5 charms, you would multiply 0.5 by the cost of one charm, which is $2.32.

Q: Can I use the cost function to find the cost of a single charm?

A: Yes, you can use the cost function to find the cost of a single charm. To do this, you would set $x$ equal to 1 and solve for $y$ . In this case, $y = 2.32 \times 1 = 2.32$ , which is the cost of one charm.

Q: What if the cost of one charm changes? Do I need to update the cost function?

A: Yes, if the cost of one charm changes, you will need to update the cost function. To do this, you would simply replace the old cost with the new cost and recalculate the function.

Q: Can I use the cost function to compare the cost of different charms?

A: Yes, you can use the cost function to compare the cost of different charms. For example, if you want to compare the cost of a charm that costs $2.32 with a charm that costs $3.00, you would simply compare the two costs.

Q: What are some real-world applications of the cost function?

A: The cost function has numerous real-world applications, such as:

Business: Companies use cost functions to determine the total cost of producing a certain number of products.
Economics: Economists use cost functions to analyze the relationship between the quantity of a good or service and its cost.
Finance: Financial analysts use cost functions to determine the total cost of investing in a particular asset.

Conclusion

In conclusion, the cost function is a powerful tool that can be used to find the total cost of buying a certain number of items. By understanding the cost function, you can make informed decisions about your purchases and compare the cost of different charms.