The Original Value of the Home

Oct 13, 2025 by windailys.com 52 views

Introduction

In this article, we will explore how to model the decrease in value of a home over time. We will use a mathematical equation to represent the situation and select the correct equation that models the situation after a certain number of years.

The Original Value of the Home

The original value of the home is $249,000. This is the initial value of the home before any decrease in value.

The Rate of Decrease

The value of the home decreases by 7.1% each year. This means that the value of the home is reduced by 7.1% of its original value each year.

Selecting the Correct Equation

To model the decrease in value of the home, we need to select the correct equation that represents the situation. The equation should take into account the original value of the home and the rate of decrease.

Option A: $ V(t) = 249,000(1 - 0.071)^t $

This equation represents the value of the home after t years. The value of the home is multiplied by (1 - 0.071), which represents the rate of decrease. The result is raised to the power of t, which represents the number of years.

Option B: $ V(t) = 249,000(1 + 0.071)^t $

This equation also represents the value of the home after t years. However, the rate of decrease is represented by (1 + 0.071), which is incorrect. The rate of decrease should be represented by (1 - 0.071).

Option C: $ V(t) = 249,000(0.071)^t $

This equation represents the value of the home after t years. However, the rate of decrease is represented by 0.071, which is the decimal form of 7.1%. The correct representation of the rate of decrease is (1 - 0.071).

Conclusion

Based on the analysis above, the correct equation that models the situation is:

$ V(t) = 249,000(1 - 0.071)^t $

This equation represents the value of the home after t years, taking into account the original value of the home and the rate of decrease.

Why This Equation is Correct

This equation is correct because it represents the value of the home after t years, taking into account the original value of the home and the rate of decrease. The value of the home is multiplied by (1 - 0.071), which represents the rate of decrease. The result is raised to the power of t, which represents the number of years.

How to Use This Equation

To use this equation, simply plug in the value of t, which represents the number of years. For example, if you want to find the value of the home after 5 years, you would plug in t = 5.

Example

Suppose you want to find the value of the home after 5 years. You would plug in t = 5 into the equation:

$ V(5) = 249,000(1 - 0.071)^5 $

Simplifying the equation, you get:

$ V(5) = 249,000(0.929)^5 $

Evaluating the expression, you get:

$ V(5) = 216,919.19 $

Therefore, the value of the home after 5 years is approximately $216,919.19.

Conclusion

Q: What is the formula for calculating the value of a home after a certain number of years?

A: The formula for calculating the value of a home after a certain number of years is:

$ V(t) = 249,000(1 - 0.071)^t $

This formula represents the value of the home after t years, taking into account the original value of the home and the rate of decrease.

Q: What is the rate of decrease in the value of the home?

A: The rate of decrease in the value of the home is 7.1% per year.

Q: How do I use the formula to calculate the value of the home after a certain number of years?

A: To use the formula, simply plug in the value of t, which represents the number of years. For example, if you want to find the value of the home after 5 years, you would plug in t = 5.

Q: What is the value of the home after 5 years?

A: To find the value of the home after 5 years, you would plug in t = 5 into the formula:

$ V(5) = 249,000(1 - 0.071)^5 $

Simplifying the equation, you get:

$ V(5) = 249,000(0.929)^5 $

Evaluating the expression, you get:

$ V(5) = 216,919.19 $

Therefore, the value of the home after 5 years is approximately $216,919.19.

Q: What happens if the rate of decrease is not 7.1% per year?

A: If the rate of decrease is not 7.1% per year, you would need to adjust the formula accordingly. For example, if the rate of decrease is 5% per year, the formula would be:

$ V(t) = 249,000(1 - 0.05)^t $

Q: Can I use this formula to calculate the value of any asset?

A: No, this formula is specifically designed to calculate the value of a home after a certain number of years, taking into account the original value of the home and the rate of decrease. You would need to use a different formula to calculate the value of other assets.

Q: What is the significance of the exponent t in the formula?

A: The exponent t represents the number of years. It is used to calculate the value of the home after a certain number of years.

Q: Can I use a calculator to calculate the value of the home after a certain number of years?

A: Yes, you can use a calculator to calculate the value of the home after a certain number of years. Simply plug in the values of the original value of the home, the rate of decrease, and the number of years, and the calculator will give you the result.

Q: What is the relationship between the formula and the concept of depreciation?

A: The formula is related to the concept of depreciation, which is the decrease in value of an asset over time. The formula calculates the value of the home after a certain number of years, taking into account the original value of the home and the rate of decrease, which is a key concept in depreciation.