Yolanda Wants To Save $\$500$ To Buy A TV. She Saves $\$18$ Each Week. The Amount, $A$ (in Dollars), That She Still Needs After $w$ Weeks Is Given By The Function:$A(w) = 500 - 18w$Answer The Following

by ADMIN 202 views

Introduction

In today's world, saving money is essential for achieving financial goals. Whether it's buying a new TV, a car, or a house, having a clear understanding of one's savings plan is crucial. In this article, we will explore Yolanda's savings plan, which involves saving $18\$18 each week to buy a TV worth $500\$500. We will use mathematical functions to model her savings and analyze the amount she still needs after a certain number of weeks.

The Savings Function

The amount, AA (in dollars), that Yolanda still needs after ww weeks is given by the function:

A(w)=500−18wA(w) = 500 - 18w

This function represents the amount of money Yolanda needs to save after a certain number of weeks. The variable ww represents the number of weeks, and the constant 500500 represents the total amount she needs to save. The coefficient −18-18 represents the amount she saves each week.

Understanding the Function

To understand the function, let's break it down into its components. The function has two main parts: the constant term and the variable term. The constant term, 500500, represents the initial amount Yolanda needs to save. The variable term, −18w-18w, represents the amount she saves each week.

When w=0w = 0, the function becomes A(0)=500−18(0)=500A(0) = 500 - 18(0) = 500. This means that Yolanda needs to save $500\$500 initially.

When w=1w = 1, the function becomes A(1)=500−18(1)=482A(1) = 500 - 18(1) = 482. This means that after one week, Yolanda needs to save $482\$482.

When w=2w = 2, the function becomes A(2)=500−18(2)=464A(2) = 500 - 18(2) = 464. This means that after two weeks, Yolanda needs to save $464\$464.

As we can see, the function decreases by $18\$18 each week, representing the amount Yolanda saves each week.

Graphing the Function

To visualize the function, we can graph it on a coordinate plane. The x-axis represents the number of weeks, and the y-axis represents the amount Yolanda needs to save.

import matplotlib.pyplot as plt
import numpy as np

# Define the function
def A(w):
    return 500 - 18 * w

# Generate x values
w = np.linspace(0, 20, 100)

# Generate y values
A_values = A(w)

# Plot the function
plt.plot(w, A_values)
plt.xlabel('Number of Weeks')
plt.ylabel('Amount Needed')
plt.title('Yolanda\'s Savings Plan')
plt.grid(True)
plt.show()

The graph shows a linear decrease in the amount Yolanda needs to save each week.

Interpreting the Graph

The graph shows that the amount Yolanda needs to save decreases linearly each week. This means that if she continues to save $18\$18 each week, she will reach her goal of saving $500\$500 in 27.78 weeks (or approximately 6.67 months).

Conclusion

In conclusion, Yolanda's savings plan can be modeled using a linear function. The function represents the amount she still needs to save after a certain number of weeks. By analyzing the function, we can see that she needs to save $18\$18 each week to reach her goal of saving $500\$500. The graph of the function shows a linear decrease in the amount she needs to save each week.

Real-World Applications

Yolanda's savings plan has real-world applications in personal finance. By understanding the concept of linear functions, individuals can create their own savings plans and track their progress. This can help them achieve their financial goals and make informed decisions about their money.

Future Research

Future research can explore the application of linear functions in other areas of personal finance, such as investing and budgeting. By analyzing the relationships between variables, individuals can make informed decisions about their financial resources and achieve their goals.

References

Appendix

The following is a list of formulas and equations used in this article:

  • A(w)=500−18wA(w) = 500 - 18w
  • A(0)=500−18(0)=500A(0) = 500 - 18(0) = 500
  • A(1)=500−18(1)=482A(1) = 500 - 18(1) = 482
  • A(2)=500−18(2)=464A(2) = 500 - 18(2) = 464

Introduction

In our previous article, we explored Yolanda's savings plan, which involves saving $18\$18 each week to buy a TV worth $500\$500. We used mathematical functions to model her savings and analyzed the amount she still needs after a certain number of weeks. In this article, we will answer some frequently asked questions about Yolanda's savings plan.

Q&A

Q: How much does Yolanda need to save each week?

A: Yolanda needs to save $18\$18 each week to reach her goal of saving $500\$500.

Q: How many weeks will it take Yolanda to save $500\$500?

A: It will take Yolanda approximately 27.78 weeks (or 6.67 months) to save $500\$500 if she continues to save $18\$18 each week.

Q: What happens if Yolanda saves more than $18\$18 each week?

A: If Yolanda saves more than $18\$18 each week, she will reach her goal of saving $500\$500 in fewer weeks.

Q: What happens if Yolanda saves less than $18\$18 each week?

A: If Yolanda saves less than $18\$18 each week, she will take longer to reach her goal of saving $500\$500.

Q: Can Yolanda's savings plan be changed?

A: Yes, Yolanda's savings plan can be changed. For example, she could increase her weekly savings amount or decrease it.

Q: How can Yolanda's savings plan be visualized?

A: Yolanda's savings plan can be visualized using a graph, which shows a linear decrease in the amount she needs to save each week.

Q: What are the real-world applications of Yolanda's savings plan?

A: The real-world applications of Yolanda's savings plan include personal finance, investing, and budgeting.

Q: Can Yolanda's savings plan be used to model other financial goals?

A: Yes, Yolanda's savings plan can be used to model other financial goals, such as saving for a car or a house.

Conclusion

In conclusion, Yolanda's savings plan is a simple yet effective way to model her financial goals. By understanding the concept of linear functions, individuals can create their own savings plans and track their progress. This can help them achieve their financial goals and make informed decisions about their money.

Real-World Applications

Yolanda's savings plan has real-world applications in personal finance. By understanding the concept of linear functions, individuals can create their own savings plans and track their progress. This can help them achieve their financial goals and make informed decisions about their money.

Future Research

Future research can explore the application of linear functions in other areas of personal finance, such as investing and budgeting. By analyzing the relationships between variables, individuals can make informed decisions about their financial resources and achieve their goals.

References

Appendix

The following is a list of formulas and equations used in this article:

  • A(w)=500−18wA(w) = 500 - 18w
  • A(0)=500−18(0)=500A(0) = 500 - 18(0) = 500
  • A(1)=500−18(1)=482A(1) = 500 - 18(1) = 482
  • A(2)=500−18(2)=464A(2) = 500 - 18(2) = 464

Note: The formulas and equations are listed in the appendix for reference purposes only.

Additional Resources

For more information on Yolanda's savings plan, please visit the following resources:

  • Khan Academy: Linear Functions
  • Investopedia: Savings Plan
  • The Balance: Savings Plan

Note: The resources listed above are for informational purposes only and are not affiliated with this article.