A Car Purchased For $ 10 , 000 \$10,000 $10 , 000 Depreciates Under A Straight-line Method By $ 750 \$750 $750 Each Year. Which Equation Below Best Models This Depreciation?A. Y = 10000 + 750 X Y = 10000 + 750x Y = 10000 + 750 X B. Y = 10000 − 750 X Y = 10000 - 750x Y = 10000 − 750 X C. $y = 10000x +

Introduction

Depreciation is a fundamental concept in mathematics, particularly in the field of finance. It refers to the decrease in value of an asset over time, often due to wear and tear, obsolescence, or other factors. In this article, we will explore the straight-line method of depreciation, which is a common approach used to calculate the decrease in value of an asset over a specific period.

What is the Straight-Line Method?

The straight-line method is a simple and straightforward approach to calculating depreciation. It assumes that the asset loses its value at a constant rate over a fixed period. In other words, the asset depreciates by the same amount each year. This method is often used for assets with a relatively short lifespan, such as cars, computers, or other equipment.

The Equation for Straight-Line Depreciation

The equation for straight-line depreciation is given by:

y = initial value - (initial value * rate of depreciation * time)

where:

• y is the value of the asset at the end of the depreciation period
• initial value is the original value of the asset
• rate of depreciation is the percentage decrease in value per year
• time is the number of years the asset has been in use

Applying the Straight-Line Method to a Car

Let's consider a car purchased for $\$10,000$ that depreciates by $\$750$ each year. We can use the equation above to model this depreciation.

Option A: $y = 10000 + 750x$

This equation suggests that the value of the car increases by $\$750$ each year, which is not consistent with the straight-line method. The correct equation should show a decrease in value over time.

Option B: $y = 10000 - 750x$

This equation suggests that the value of the car decreases by $\$750$ each year, which is consistent with the straight-line method. The initial value of the car is $\$10,000$, and the rate of depreciation is $\$750$ per year.

Option C: $y = 10000x +$

This equation is incomplete and does not accurately represent the straight-line method of depreciation.

Conclusion

Based on the analysis above, the equation that best models the depreciation of a car purchased for $\$10,000$ that depreciates by $\$750$ each year is:

y = 10000 - 750x

This equation accurately represents the straight-line method of depreciation, where the value of the car decreases by $\$750$ each year.

Example Use Case

Suppose we want to calculate the value of the car after 5 years. We can plug in the values into the equation:

y = 10000 - 750(5) y = 10000 - 3750 y = 6250

Therefore, the value of the car after 5 years is $\$6,250$.

Tips and Tricks

• When using the straight-line method, make sure to calculate the rate of depreciation accurately.
• The straight-line method assumes that the asset loses its value at a constant rate over a fixed period.
• The equation for straight-line depreciation is given by: y = initial value - (initial value * rate of depreciation * time)

Frequently Asked Questions

• What is the-line method of depreciation? The straight-line method is a simple and straightforward approach to calculating depreciation, where the asset loses its value at a constant rate over a fixed period.
• How do I calculate the value of an asset using the straight-line method? To calculate the value of an asset using the straight-line method, you need to know the initial value of the asset, the rate of depreciation, and the time period. You can then use the equation: y = initial value - (initial value * rate of depreciation * time) to calculate the value of the asset.

Conclusion

In conclusion, the straight-line method of depreciation is a simple and effective approach to calculating the decrease in value of an asset over time. By using the equation y = 10000 - 750x, we can accurately model the depreciation of a car purchased for $\$10,000$ that depreciates by $\$750$ each year.

Introduction

In our previous article, we explored the straight-line method of depreciation, which is a common approach used to calculate the decrease in value of an asset over a specific period. We also discussed the equation for straight-line depreciation and applied it to a car purchased for $\$10,000$ that depreciates by $\$750$ each year. In this article, we will answer some frequently asked questions related to the straight-line method of depreciation.

Q&A

Q1: What is the straight-line method of depreciation?

A1: The straight-line method is a simple and straightforward approach to calculating depreciation, where the asset loses its value at a constant rate over a fixed period.

Q2: How do I calculate the value of an asset using the straight-line method?

A2: To calculate the value of an asset using the straight-line method, you need to know the initial value of the asset, the rate of depreciation, and the time period. You can then use the equation: y = initial value - (initial value * rate of depreciation * time) to calculate the value of the asset.

Q3: What is the difference between the straight-line method and other methods of depreciation?

A3: The straight-line method assumes that the asset loses its value at a constant rate over a fixed period. Other methods of depreciation, such as the declining balance method, assume that the asset loses its value at a decreasing rate over time.

Q4: Can I use the straight-line method for assets with a long lifespan?

A4: While the straight-line method can be used for assets with a long lifespan, it may not be the most accurate method. For assets with a long lifespan, it may be more accurate to use the declining balance method or another method that takes into account the asset's decreasing value over time.

Q5: How do I determine the rate of depreciation for an asset?

A5: The rate of depreciation for an asset can be determined by considering the asset's lifespan, its initial value, and its expected useful life. For example, if an asset has a lifespan of 5 years and an initial value of $\$10,000$, the rate of depreciation might be $\$2,000$ per year.

Q6: Can I use the straight-line method for assets that are subject to wear and tear?

A6: While the straight-line method can be used for assets that are subject to wear and tear, it may not be the most accurate method. For assets that are subject to wear and tear, it may be more accurate to use the declining balance method or another method that takes into account the asset's decreasing value over time.

Q7: How do I calculate the value of an asset after a certain period of time using the straight-line method?

A7: To calculate the value of an asset after a certain period of time using the straight-line method, you can use the equation: y = initial value - (initial value * rate of depreciation * time). For example, if an asset has an initial value of $\$10,000$, a rate of depreciation of $\$750$ per year, and a time period of 5 years, the value of the asset after 5 years would be: y = 10000 - (10000 \ 0.075 * 5) = 6250.

Q8: Can I use the straight-line method for assets that are subject to obsolescence?

A8: While the straight-line method can be used for assets that are subject to obsolescence, it may not be the most accurate method. For assets that are subject to obsolescence, it may be more accurate to use the declining balance method or another method that takes into account the asset's decreasing value over time.

Conclusion

In conclusion, the straight-line method of depreciation is a simple and effective approach to calculating the decrease in value of an asset over time. By understanding the equation for straight-line depreciation and answering some frequently asked questions, you can accurately model the depreciation of an asset and make informed decisions about its value.

Example Use Case

Suppose we want to calculate the value of a car after 10 years using the straight-line method. We can use the equation: y = initial value - (initial value * rate of depreciation * time). If the car has an initial value of $\$10,000$, a rate of depreciation of $\$750$ per year, and a time period of 10 years, the value of the car after 10 years would be: y = 10000 - (10000 * 0.075 * 10) = 3750.

Tips and Tricks

• When using the straight-line method, make sure to calculate the rate of depreciation accurately.
• The straight-line method assumes that the asset loses its value at a constant rate over a fixed period.
• The equation for straight-line depreciation is given by: y = initial value - (initial value * rate of depreciation * time)

Frequently Asked Questions

• What is the straight-line method of depreciation? The straight-line method is a simple and straightforward approach to calculating depreciation, where the asset loses its value at a constant rate over a fixed period.
• How do I calculate the value of an asset using the straight-line method? To calculate the value of an asset using the straight-line method, you need to know the initial value of the asset, the rate of depreciation, and the time period. You can then use the equation: y = initial value - (initial value * rate of depreciation * time) to calculate the value of the asset.

Conclusion

In conclusion, the straight-line method of depreciation is a simple and effective approach to calculating the decrease in value of an asset over time. By understanding the equation for straight-line depreciation and answering some frequently asked questions, you can accurately model the depreciation of an asset and make informed decisions about its value.