The Function Below Represents The Interest Jessi Earns On An Investment. Identify The Term That Represents The Amount Of Money Originally Invested. F ( X ) = 1 , 000 ( 1 + 0.05 ) X F(x) = 1,000(1+0.05)^x F ( X ) = 1 , 000 ( 1 + 0.05 ) X A. 1,000 B. 1 C. 0.05 D. 1.05

Understanding the Function

The given function, $f(x) = 1,000(1+0.05)^x$, represents the interest Jessi earns on an investment. To identify the term that represents the amount of money originally invested, we need to understand the components of the function.

Breaking Down the Function

The function is in the form of $f(x) = P(1 + r)^x$, where:

• $P$ is the principal amount (the original investment)
• $r$ is the rate of interest
• $x$ is the number of years the money is invested

Identifying the Original Investment Amount

In the given function, $f(x) = 1,000(1+0.05)^x$, we can see that the principal amount $P$ is represented by the term $1,000$. This is the amount of money originally invested.

Why 1,000 Represents the Original Investment Amount

The term $1,000$ is the initial amount that is multiplied by the growth factor $(1+0.05)^x$. This means that the interest earned is calculated based on the original investment of $1,000.

Eliminating Incorrect Options

Let's eliminate the other options:

• Option B (1): This is the growth factor, not the original investment amount.
• Option C (0.05): This is the rate of interest, not the original investment amount.
• Option D (1.05): This is the growth factor plus one, not the original investment amount.

Conclusion

In conclusion, the term that represents the amount of money originally invested is Option A (1,000).

Understanding the Importance of Identifying the Original Investment Amount

Identifying the original investment amount is crucial in understanding the function of interest earned on an investment. It helps in calculating the interest earned and making informed decisions about investments.

Real-World Applications

The concept of identifying the original investment amount has real-world applications in finance, economics, and business. It is essential in calculating returns on investment, determining the value of an investment, and making informed decisions about investments.

Example Use Case

Suppose Jessi invests $1,000 in a savings account with a 5% annual interest rate. After 5 years, the interest earned can be calculated using the function $f(x) = 1,000(1+0.05)^x$. By identifying the original investment amount, Jessi can determine the interest earned and make informed decisions about her investments.

Conclusion

Frequently Asked Questions

Q: What is the function of interest earned on an investment?

A: The function of interest earned on an investment is represented by the equation $f(x) = P(1 + r)^x$, where $P$ is the principal amount (the original investment), $r$ is the rate of interest, and $x$ is the number of years the money is invested.

Q: What is the principal amount in the given function?

A: In the given function, $f(x) = 1,000(1+0.05)^x$, the principal amount $P$ is represented by the term $1,000$. This is the amount of money originally invested.

Q: What is the rate of interest in the given function?

A: In the given function, $f(x) = 1,000(1+0.05)^x$, the rate of interest $r$ is represented by the term $0.05$. This is the rate at which the interest is earned.

Q: How is the interest earned calculated?

A: The interest earned is calculated by multiplying the principal amount by the growth factor $(1 + r)^x$. In the given function, the interest earned is calculated by multiplying $1,000$ by $(1+0.05)^x$.

Q: What is the growth factor in the given function?

A: In the given function, $f(x) = 1,000(1+0.05)^x$, the growth factor is represented by the term $(1+0.05)^x$. This is the factor by which the principal amount is multiplied to calculate the interest earned.

Q: How can I use this function to calculate the interest earned on an investment?

A: To calculate the interest earned on an investment, you can use the function $f(x) = P(1 + r)^x$ and plug in the values of $P$, $r$, and $x$. For example, if you invest $1,000 at a 5% annual interest rate for 5 years, you can calculate the interest earned by plugging in $P = 1,000$, $r = 0.05$, and $x = 5$.

Q: What are some real-world applications of this function?

A: The function of interest earned on an investment has real-world applications in finance, economics, and business. It is used to calculate returns on investment, determine the value of an investment, and make informed decisions about investments.

Q: Can I use this function to calculate the interest earned on a savings account?

A: Yes, you can use this function to calculate the interest earned on a savings account. Simply plug in the values of the principal amount, interest rate, and time period, and the function will calculate the interest earned.

Q: What are some common mistakes to avoid when using this function?

A: Some common mistakes to avoid when using this function include:

• Not understanding the components of the function (principal amount, rate of interest, and time period)
• Not plugging in the correct values for the principal amount, rate of interest, and time period
• Not calculating the interest earned correctly
• Not considering compounding interest

Q: How can I make informed decisions about investments using this function?

A: To make informed decisions about investments using this function, you should:

• Understand the components of the function and how they affect the interest earned
• Plug in the correct values for the principal amount, rate of interest, and time period
• Calculate the interest earned correctly
• Consider compounding interest
• Compare the interest earned on different investments to make informed decisions

Conclusion

In conclusion, the function of interest earned on an investment is a powerful tool for calculating returns on investment and making informed decisions about investments. By understanding the components of the function and using it correctly, you can make informed decisions about investments and achieve your financial goals.