The Function $p(x)=-2(x-9)^2+100$ Is Used To Determine The Profit On T-shirts Sold For $x$ Dollars. What Would The Profit From Sales Be If The Price Of The T-shirts Were $\$15$ Apiece?A. \$15 B. \$28 C. \$172

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Introduction

In the world of business, understanding the relationship between price and profit is crucial for making informed decisions. One way to visualize this relationship is through the use of a quadratic function, which can be used to model the profit on T-shirts sold for a given price. In this article, we will explore the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 and use it to determine the profit from sales if the price of the T-shirts were $15\$15 apiece.

Understanding the Function

The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 is a quadratic function that represents the profit on T-shirts sold for a given price. The function has a negative coefficient of −2-2, which indicates that the profit decreases as the price increases. The function also has a vertex at (9,100)(9, 100), which represents the maximum profit that can be achieved.

Finding the Profit at a Given Price

To find the profit at a given price, we need to substitute the price into the function and solve for the profit. In this case, we want to find the profit if the price of the T-shirts were $15\$15 apiece. We can substitute x=15x=15 into the function and solve for the profit.

Calculating the Profit

To calculate the profit, we need to substitute x=15x=15 into the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100. This gives us:

p(15)=−2(15−9)2+100p(15)=-2(15-9)^2+100

Expanding the squared term, we get:

p(15)=−2(6)2+100p(15)=-2(6)^2+100

Simplifying the expression, we get:

p(15)=−2(36)+100p(15)=-2(36)+100

p(15)=−72+100p(15)=-72+100

p(15)=28p(15)=28

Conclusion

In conclusion, the profit from sales if the price of the T-shirts were $15\$15 apiece would be $28\$28. This is based on the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100, which represents the profit on T-shirts sold for a given price. The function has a negative coefficient of −2-2, which indicates that the profit decreases as the price increases. The function also has a vertex at (9,100)(9, 100), which represents the maximum profit that can be achieved.

Discussion

The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 is a quadratic function that represents the profit on T-shirts sold for a given price. The function has a negative coefficient of −2-2, which indicates that the profit decreases as the price increases. The function also has a vertex at (9,100)(9, 100), which represents the maximum profit that can be achieved.

The profit from sales if the price of the T-shirts were $15\$15 apiece would be $28\$28. This is based on the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100, which represents the profit on T-shirts sold for a given price.

Applications

The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 has several applications in business and economics. For example, it can be used to model the profit on T-shirts sold for a given price, as we have seen in this article. It can also be used to model the profit on other products, such as clothing, electronics, and more.

Limitations

The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 has several limitations. For example, it assumes that the profit decreases as the price increases, which may not always be the case. It also assumes that the function is quadratic, which may not always be the case.

Future Research

Future research on the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 could involve exploring its applications in business and economics. It could also involve exploring its limitations and how they can be addressed.

Conclusion

In conclusion, the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 is a quadratic function that represents the profit on T-shirts sold for a given price. The function has a negative coefficient of −2-2, which indicates that the profit decreases as the price increases. The function also has a vertex at (9,100)(9, 100), which represents the maximum profit that can be achieved. The profit from sales if the price of the T-shirts were $15\$15 apiece would be $28\$28. This is based on the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100, which represents the profit on T-shirts sold for a given price.

Introduction

In our previous article, we explored the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 and used it to determine the profit from sales if the price of the T-shirts were $15\$15 apiece. In this article, we will answer some of the most frequently asked questions about the function and its applications.

Q&A

Q: What is the purpose of the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100?

A: The purpose of the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 is to model the profit on T-shirts sold for a given price. It can be used to determine the profit from sales at a given price.

Q: What is the vertex of the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100?

A: The vertex of the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 is at (9,100)(9, 100). This represents the maximum profit that can be achieved.

Q: What is the coefficient of the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100?

A: The coefficient of the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 is −2-2. This indicates that the profit decreases as the price increases.

Q: Can the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 be used to model the profit on other products?

A: Yes, the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 can be used to model the profit on other products, such as clothing, electronics, and more.

Q: What are the limitations of the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100?

A: The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 assumes that the profit decreases as the price increases, which may not always be the case. It also assumes that the function is quadratic, which may not always be the case.

Q: Can the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 be used to make predictions about future sales?

A: Yes, the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 can be used to make predictions about future sales. However, it is essential to consider the limitations of the function and the assumptions that it makes.

Q: How can the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 be used in real-world applications?

A: The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 can be used in real-world applications such as:

  • Modeling the profit on T-shirts sold for a given price
  • Determining the optimal price for a product
  • Making predictions about future sales
  • Analyzing the relationship between price and profit

Conclusion

In conclusion, the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 is a quadratic function that represents the profit on T-shirts sold for a given price. It has a negative coefficient of −2-2, which indicates that the profit decreases as the price increases. The function also has a vertex at (9,100)(9, 100), which represents the maximum profit that can be achieved. The profit from sales if the price of the T-shirts were $15\$15 apiece would be $28\$28. This is based on the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100, which represents the profit on T-shirts sold for a given price.

Discussion

The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 has several applications in business and economics. For example, it can be used to model the profit on T-shirts sold for a given price, as we have seen in this article. It can also be used to model the profit on other products, such as clothing, electronics, and more.

Applications

The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 has several applications in business and economics. For example, it can be used to:

  • Model the profit on T-shirts sold for a given price
  • Determine the optimal price for a product
  • Make predictions about future sales
  • Analyze the relationship between price and profit

Limitations

The function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 has several limitations. For example, it assumes that the profit decreases as the price increases, which may not always be the case. It also assumes that the function is quadratic, which may not always be the case.

Future Research

Future research on the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 could involve exploring its applications in business and economics. It could also involve exploring its limitations and how they can be addressed.

Conclusion

In conclusion, the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100 is a quadratic function that represents the profit on T-shirts sold for a given price. It has a negative coefficient of −2-2, which indicates that the profit decreases as the price increases. The function also has a vertex at (9,100)(9, 100), which represents the maximum profit that can be achieved. The profit from sales if the price of the T-shirts were $15\$15 apiece would be $28\$28. This is based on the function p(x)=−2(x−9)2+100p(x)=-2(x-9)^2+100, which represents the profit on T-shirts sold for a given price.