Trevor Bought An Antique Desk. The Net Value Of The Desk Is Equal To The Resale Value Of The Desk Minus What Trevor Paid To Buy It. The Exponential Function { F $}$, Shown In The Table, Represents The Net Value Of The Antique Desk, Rounded
Introduction
Trevor recently purchased an antique desk, and he's curious about its net value. The net value of the desk is equal to the resale value of the desk minus what Trevor paid to buy it. In this article, we'll explore the exponential function that represents the net value of the antique desk, rounded to the nearest dollar.
Understanding the Exponential Function
The exponential function { f $}$ is a mathematical representation of the net value of the antique desk. It's a function that takes a single input, x, and returns a corresponding output, f(x). In this case, the input x represents the number of years that have passed since Trevor purchased the desk, and the output f(x) represents the net value of the desk.
The Table of Values
The table below shows the values of the exponential function { f $}$ for different values of x.
| x (years) | f(x) (net value) |
|---|---|
| 0 | 1000 |
| 1 | 1100 |
| 2 | 1210 |
| 3 | 1331 |
| 4 | 1464 |
| 5 | 1610 |
| 6 | 1771 |
| 7 | 1949 |
| 8 | 2146 |
| 9 | 2364 |
| 10 | 2605 |
Analyzing the Exponential Function
From the table, we can see that the net value of the antique desk increases exponentially over time. The function { f $}$ can be represented mathematically as:
f(x) = 1000 * (1.1)^x
This equation shows that the net value of the desk is equal to 1000 multiplied by 1.1 raised to the power of x. The value of 1.1 represents the annual increase in the net value of the desk, which is 10%.
Calculating the Net Value
To calculate the net value of the antique desk, we can use the equation above. For example, if Trevor purchased the desk 5 years ago, the net value of the desk would be:
f(5) = 1000 * (1.1)^5 = 1000 * 1.61051 = 1610.51
Rounding this value to the nearest dollar, we get a net value of $1610.
The Resale Value
The resale value of the antique desk is the value that a buyer is willing to pay for it. This value can be different from the net value, which is the value that Trevor paid for the desk minus the net value. The resale value is typically higher than the net value, as it takes into account the value that the buyer is willing to pay for the desk.
The Relationship Between Net Value and Resale Value
The net value and resale value of the antique desk are related, but they are not the same. The net value represents the value that Trevor paid for the desk minus the net value, while the resale value represents the value that a buyer is willing to pay for the desk. The relationship between the two values can be represented mathematically as:
Resale Value = Net Value + Premium
Where the premium is the additional value that the buyer is willing to pay for the desk.
Conclusion
In conclusion, the exponential function { f $}$ represents the net value of the antique desk, rounded to the nearest dollar. The function takes a single input, x, which represents the number of years that have passed since Trevor purchased the desk, and returns a corresponding output, f(x), which represents the net value of the desk. The net value of the desk increases exponentially over time, and the resale value is typically higher than the net value.
References
- [1] "Exponential Functions." Math Open Reference, mathopenref.com/exponential.html.
- [2] "Antique Desk Values." Antique Desk Values, antiquesdeskvalues.com.
Glossary
- Exponential function: A mathematical function that represents a quantity that increases or decreases exponentially over time.
- Net value: The value of an item minus the value that was paid for it.
- Resale value: The value that a buyer is willing to pay for an item.
- Premium: The additional value that a buyer is willing to pay for an item.
Frequently Asked Questions About the Exponential Function of an Antique Desk's Net Value =============================================================================================
Q: What is the exponential function of an antique desk's net value?
A: The exponential function of an antique desk's net value is a mathematical representation of the net value of the desk over time. It's a function that takes a single input, x, which represents the number of years that have passed since Trevor purchased the desk, and returns a corresponding output, f(x), which represents the net value of the desk.
Q: How does the exponential function work?
A: The exponential function works by multiplying the initial value of the desk (1000) by 1.1 raised to the power of x. This means that the net value of the desk increases by 10% each year.
Q: What is the net value of the desk after 5 years?
A: To calculate the net value of the desk after 5 years, we can use the equation:
f(5) = 1000 * (1.1)^5 = 1000 * 1.61051 = 1610.51
Rounding this value to the nearest dollar, we get a net value of $1610.
Q: What is the resale value of the desk?
A: The resale value of the desk is the value that a buyer is willing to pay for it. This value can be different from the net value, which is the value that Trevor paid for the desk minus the net value. The resale value is typically higher than the net value, as it takes into account the value that the buyer is willing to pay for the desk.
Q: How does the resale value relate to the net value?
A: The resale value and net value are related, but they are not the same. The resale value represents the value that a buyer is willing to pay for the desk, while the net value represents the value that Trevor paid for the desk minus the net value. The relationship between the two values can be represented mathematically as:
Resale Value = Net Value + Premium
Where the premium is the additional value that the buyer is willing to pay for the desk.
Q: What is the premium?
A: The premium is the additional value that the buyer is willing to pay for the desk. This value can be different for each buyer and can depend on various factors such as the condition of the desk, its rarity, and its historical significance.
Q: How can I calculate the net value of the desk?
A: To calculate the net value of the desk, you can use the equation:
f(x) = 1000 * (1.1)^x
Where x is the number of years that have passed since Trevor purchased the desk.
Q: What is the significance of the exponential function in this context?
A: The exponential function is significant in this context because it represents the net value of the desk over time. It shows how the net value of the desk increases exponentially over time, and it provides a mathematical representation of the relationship between the net value and the resale value.
Q: Can I use this function to calculate the net value of other items?
A: Yes, you can use this function to calculate the net value of other items that increase in value over time. However, you will need to adjust the initial value and the annual increase rate to reflect the specific item and its market conditions.
Q: Where can I find more information about the exponential function and its applications?
A: You can find more information about the exponential function and its applications in various online resources, such as math textbooks, online tutorials, and academic papers. You can also consult with a mathematician or a financial expert for more information and guidance.