Select The Correct Answer From Each Drop-down Menu.The Function F ( X ) = 500 ( 1 + 0.015 4 ) 4 T F(x)=500\left(1+\frac{0.015}{4}\right)^{4t} F ( X ) = 500 ( 1 + 4 0.015 ​ ) 4 T Models The Balance In A Savings Account.The Savings Account Had An Initial Balance Of □ \square □ And Compounds

The given function $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$ represents the balance in a savings account over time. To understand the initial balance and the compounding process, we need to analyze the function and its components.

Breaking Down the Function

The function $f(x)$ can be broken down into several components:

• Initial Balance: The initial balance in the savings account is represented by the constant term $500$. This is the starting balance in the account.
• Compounding Rate: The compounding rate is represented by the term $\frac{0.015}{4}$. This is the rate at which interest is added to the account.
• Compounding Frequency: The compounding frequency is represented by the exponent $4t$. This indicates that the interest is compounded quarterly, as the exponent is $4$.

Understanding the Compounding Process

The compounding process in the savings account can be understood by analyzing the term $\left(1+\frac{0.015}{4}\right)^{4t}$. This term represents the growth factor, which is the ratio of the final balance to the initial balance.

• Growth Factor: The growth factor is calculated as $\left(1+\frac{0.015}{4}\right)^{4t}$. This represents the increase in the balance due to the compounding of interest.
• Compounding Period: The compounding period is represented by the exponent $4t$. This indicates that the interest is compounded quarterly, and the exponent $4$ represents the number of times the interest is compounded in a year.

Calculating the Initial Balance

To calculate the initial balance, we need to analyze the function $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$. The initial balance is represented by the constant term $500$, which is the starting balance in the account.

Calculating the Compounding Rate

To calculate the compounding rate, we need to analyze the term $\frac{0.015}{4}$. This term represents the rate at which interest is added to the account.

Calculating the Compounding Frequency

To calculate the compounding frequency, we need to analyze the exponent $4t$. This term represents the number of times the interest is compounded in a year.

Solving for the Initial Balance

To solve for the initial balance, we need to set the function $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$ equal to the initial balance and solve for $t$.

Solving for the Compounding Rate

To solve for the compounding rate, we need to analyze the term $\frac{0.015}{4}$. This term represents the rate at which interest is added to the account.

Solving for the Compounding Frequency

To solve for the compounding frequency, we need to analyze the exponent $4t$. This term represents the number of times the interest is compounded in a year.

Conclusion

In conclusion, the function $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$ represents the balance in a savings account over time. The initial balance is represented by the constant term $500$, and the compounding rate is represented by the term $\frac{0.015}{4}$. The compounding frequency is represented by the exponent $4t$, which indicates that the interest is compounded quarterly.

Final Answer

In the previous article, we discussed the function $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$, which represents the balance in a savings account over time. Here, we will answer some frequently asked questions related to the savings account model.

Q: What is the initial balance in the savings account?

A: The initial balance in the savings account is represented by the constant term $500$. This is the starting balance in the account.

Q: What is the compounding rate in the savings account?

A: The compounding rate in the savings account is represented by the term $\frac{0.015}{4}$. This is the rate at which interest is added to the account.

Q: How often is the interest compounded in the savings account?

A: The interest is compounded quarterly in the savings account. This is represented by the exponent $4t$ in the function $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$.

Q: What is the growth factor in the savings account?

A: The growth factor in the savings account is calculated as $\left(1+\frac{0.015}{4}\right)^{4t}$. This represents the increase in the balance due to the compounding of interest.

Q: How can I calculate the balance in the savings account at a given time?

A: To calculate the balance in the savings account at a given time, you can plug in the value of $t$ into the function $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$. This will give you the balance in the account at that time.

Q: What is the formula for calculating the balance in the savings account?

A: The formula for calculating the balance in the savings account is $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$. This formula represents the balance in the account over time.

Q: How can I use the savings account model to make predictions about the future balance?

A: To make predictions about the future balance, you can use the savings account model to calculate the balance at a given time. You can then use this information to make predictions about the future balance.

Q: What are some common applications of the savings account model?

A: The savings account model has many common applications, including:

• Calculating the balance in a savings account over time
• Making predictions about the future balance
• Comparing the performance of different savings accounts
• Determining the optimal investment strategy

Conclusion

In conclusion, the savings account model is a powerful tool for understanding the balance in a savings account over time. By using the function $f(x)=500\left(1+\frac{0.015}{4}\right)^{4t}$, you can calculate the balance in the account at a given time and make predictions about the future balance. We hope this Q&A article has been helpful in understanding the savings account model.

Final Answer

The final answer is: $\boxed{500}$