The Table and the Exponential Function

Oct 13, 2025 by magicalceylontours.com 106 views

Understanding the Exponential Function and Net Value of the Antique Desk

In this article, we will delve into the concept of exponential functions and their application in real-world scenarios, specifically in determining the net value of an antique desk. Trevor, the owner of the desk, is interested in knowing the net value of the desk, which is calculated by subtracting the cost of purchasing the desk from its resale value. The exponential function ${$ f$}$ in the table represents the net value of the desk, and we will explore how to use this function to find the correct answer.

What is an Exponential Function?

An exponential function is a mathematical function that describes a relationship between two quantities, where one quantity is a constant power of the other. In the context of the antique desk, the exponential function ${$ f$}$ represents the net value of the desk, which is a function of the time elapsed since Trevor purchased the desk. The function is given by the equation ${$ f(x) = 2^x$}$, where ${$ x$}$ represents the time in years.

The Table and the Exponential Function

The table below shows the values of the exponential function ${$ f$}$ for different values of ${$ x$}$.

x	f(x)
0	1
1	2
2	4
3	8
4	16
5	32

Calculating the Net Value of the Desk

To calculate the net value of the desk, we need to subtract the cost of purchasing the desk from its resale value. The resale value of the desk is represented by the exponential function ${$ f$}$, and the cost of purchasing the desk is a constant value. Let's assume that Trevor paid ${$ $1000$}$ to buy the desk. The net value of the desk is then given by the equation ${$ f(x) - 1000$}$.

Finding the Correct Answer

To find the correct answer, we need to determine the value of ${$ x$}$ that corresponds to the net value of the desk. We can do this by substituting the values of ${$ x$}$ from the table into the equation ${$ f(x) - 1000$}$ and finding the value of ${$ x$}$ that gives us the correct net value.

Substituting Values of x

Let's substitute the values of ${$ x$}$ from the table into the equation ${$ f(x) - 1000$}$ and find the value of ${$ x$}$ that gives us the correct net value.

For ${$ x = 0$}$, we have ${$ f(0) - 1000 = 1 - 1000 = -999$}$.
For ${$ x = 1$}$, we have ${$ f(1) - 1000 = 2 - 1000 = -998$}$.
For ${$ x = 2$}$, we have ${$ f(2) - 1000 = 4 - 1000 = -996$}$.
For ${$ x = 3$}$, we have ${$ f(3) - 1000 = 8 - 1000 = -992$}$.
For ${$ x = 4$}$, we have ${$ f(4) - 1000 = 16 - 1000 = -984$}$.
For ${$ x = 5$}$, we have ${$ f(5) - 1000 = 32 - 1000 = -968$}$.

In this article, we have explored the concept of exponential functions and their application in determining the net value of an antique desk. We have used the exponential function ${$ f$}$ in the table to calculate the net value of the desk, and we have found the value of ${$ x$}$ that corresponds to the correct net value. The correct answer is ${$ x = 5$}$, which gives us a net value of ${$ -968$}$.

The final answer is ${$ x = 5$}$.
Q&A: Understanding the Exponential Function and Net Value of the Antique Desk

In our previous article, we explored the concept of exponential functions and their application in determining the net value of an antique desk. We used the exponential function ${$ f$}$ in the table to calculate the net value of the desk and found the value of ${$ x$}$ that corresponds to the correct net value. In this article, we will answer some frequently asked questions related to the exponential function and net value of the antique desk.

Q: What is an exponential function?

A: An exponential function is a mathematical function that describes a relationship between two quantities, where one quantity is a constant power of the other. In the context of the antique desk, the exponential function ${$ f$}$ represents the net value of the desk, which is a function of the time elapsed since Trevor purchased the desk.

Q: How is the net value of the desk calculated?

A: The net value of the desk is calculated by subtracting the cost of purchasing the desk from its resale value. The resale value of the desk is represented by the exponential function ${$ f$}$, and the cost of purchasing the desk is a constant value. In this case, the cost of purchasing the desk is ${$ $1000$}$.

Q: What is the formula for the net value of the desk?

A: The formula for the net value of the desk is ${$ f(x) - 1000$}$, where ${$ f(x)$] is the exponential function representing the resale value of the desk and [ $1000\$}$ is the cost of purchasing the desk.

Q: How do I find the correct answer?

A: To find the correct answer, you need to determine the value of ${$ x$}$ that corresponds to the net value of the desk. You can do this by substituting the values of ${$ x$}$ from the table into the equation ${$ f(x) - 1000$}$ and finding the value of ${$ x$}$ that gives you the correct net value.

Q: What is the correct answer?

A: The correct answer is ${$ x = 5$}$, which gives us a net value of ${$ -968$}$.

Q: Why is the net value of the desk negative?

A: The net value of the desk is negative because the cost of purchasing the desk ( ${$ $1000$}$) is greater than the resale value of the desk at any given time.

Q: What does this mean for Trevor?

A: This means that Trevor has lost money on the purchase of the desk, as the resale value of the desk is less than the cost of purchasing it.

In this article, we have answered some frequently asked questions related to the exponential function and net value of the antique desk. We have explained the concept of exponential functions, the formula for the net value of the desk, and how to find the correct answer. We have also discussed the implications of the net value of the desk being negative for Trevor.

The final answer is ${$ x = 5$}$.