Suppose That The Dollar Value { V(t) $}$ Of A Certain House That Is { T $}$ Years Old Is Given By The Following Exponential Function:${ V(t) = 427,500(1.09)^t }$Part 1 Of 3:(a) Find The Initial Value Of The
Introduction
In this article, we will explore the concept of an exponential function and its application in modeling the value of a house over time. The value of a house is often influenced by various factors such as its age, location, and condition. In this case, we are given an exponential function that represents the dollar value of a house that is t years old. Our goal is to find the initial value of the house, which is the value of the house when it is first purchased or built.
The Exponential Function
The exponential function given is:
This function represents the value of the house at any given time t, where t is the number of years the house has been in existence. The function is in the form of an exponential growth function, where the base is 1.09 and the initial value is 427,500.
Finding the Initial Value
To find the initial value of the house, we need to find the value of the function when t = 0. This is because the initial value is the value of the house when it is first purchased or built, which is at time t = 0.
We can find the initial value by substituting t = 0 into the function:
Since any number raised to the power of 0 is equal to 1, we have:
Therefore, the initial value of the house is $427,500.
Interpretation
The initial value of the house represents the value of the house when it is first purchased or built. This value is often referred to as the "purchase price" or "construction cost" of the house. In this case, the initial value of the house is $427,500, which means that the house was purchased or built for this amount.
Conclusion
In this article, we have explored the concept of an exponential function and its application in modeling the value of a house over time. We have found the initial value of the house, which is the value of the house when it is first purchased or built. The initial value of the house is $427,500, which represents the purchase price or construction cost of the house.
Future Articles
In the next article, we will explore how to find the rate of change of the house's value over time. We will also discuss how to use the exponential function to model the value of the house over a given period of time.
References
- [1] "Exponential Functions" by Math Open Reference
- [2] "House Value Model" by Investopedia
Related Articles
- [Part 2: Finding the Rate of Change of the House's Value](link to part 2)
- [Part 3: Modeling the Value of the House Over Time](link to part 3)
Understanding the Exponential Function of a House's Value: Q&A ===========================================================
Introduction
In our previous article, we explored the concept of an exponential function and its application in modeling the value of a house over time. We found the initial value of the house, which is the value of the house when it is first purchased or built. In this article, we will answer some frequently asked questions (FAQs) related to the exponential function of a house's value.
Q&A
Q: What is the purpose of using an exponential function to model the value of a house?
A: The purpose of using an exponential function to model the value of a house is to represent the rate at which the house's value changes over time. The exponential function takes into account the initial value of the house, the rate of change, and the time period to calculate the current value of the house.
Q: How does the exponential function account for the rate of change of the house's value?
A: The exponential function accounts for the rate of change of the house's value by using the base (1.09 in this case) to represent the rate of change. The base is raised to the power of the time period (t) to calculate the current value of the house.
Q: What is the significance of the initial value of the house?
A: The initial value of the house represents the value of the house when it is first purchased or built. This value is often referred to as the "purchase price" or "construction cost" of the house.
Q: How does the exponential function model the value of the house over time?
A: The exponential function models the value of the house over time by using the initial value, the rate of change, and the time period to calculate the current value of the house. The function takes into account the compounding effect of the rate of change over time to calculate the current value of the house.
Q: Can the exponential function be used to model the value of other assets, such as stocks or bonds?
A: Yes, the exponential function can be used to model the value of other assets, such as stocks or bonds. The function can be adjusted to account for the specific characteristics of the asset, such as its initial value, rate of change, and time period.
Q: What are some common applications of the exponential function in finance?
A: Some common applications of the exponential function in finance include modeling the value of assets, such as stocks or bonds, calculating the rate of return on investment, and determining the present value of future cash flows.
Q: How can the exponential function be used to make informed investment decisions?
A: The exponential function can be used to make informed investment decisions by modeling the value of assets, calculating the rate of return on investment, and determining the present value of future cash flows. This can help investors make more informed decisions about their investments.
Conclusion
In this article, we have answered some frequently asked questions (FAQs) related to the exponential function of a house's value. We have discussed the purpose of using an exponential function to model the value of a house, how the function accounts for the rate of change of the house's value, and the significance of the initial value of the house. We have also discussed some common applications of the exponential function in finance and how it can be used to make informed investment decisions.
Future Articles
In the next article, we will explore some advanced topics related to the exponential function, such as modeling the value of assets with multiple rates of change and calculating the present value of future cash flows.
References
- [1] "Exponential Functions" by Math Open Reference
- [2] "House Value Model" by Investopedia
Related Articles
- [Part 1: Understanding the Exponential Function of a House's Value](link to part 1)
- [Part 3: Modeling the Value of the House Over Time](link to part 3)