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Answer :
To solve this problem, we need to determine the formula that represents the amount of money in Josiah's account after a certain number of years, with the interest being compounded annually.
1. Understand the Initial Set-Up:
- Josiah initially invests [tex]$360 in the account.
- The account earns 3% interest annually.
2. Identify the Formula for Compound Interest:
- The general formula for the amount \( y \) in an account with compound interest is:
\[
y = \text{principal} \times (1 + \text{interest rate})^x
\]
- In this formula:
- The principal is the initial amount of money deposited, which is $[/tex]360.
- The interest rate is the annual interest rate (converted from a percentage to a decimal), which is [tex]\( 3\% = 0.03 \)[/tex].
- The variable [tex]\( x \)[/tex] represents the number of years the money is invested.
3. Plug in the Values into the Formula:
- Using the values provided:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
4. Simplify the Formula:
- Calculate [tex]\( 1 + 0.03 \)[/tex]:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
- Substitute back into the equation:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
The equation that represents the amount in Josiah's account after [tex]\( x \)[/tex] years, with a 3% annual interest rate, is:
[tex]\[
y = 360(1.03)^x
\][/tex]
Therefore, the correct choice is [tex]\( y=360(1.03)^x \)[/tex].
1. Understand the Initial Set-Up:
- Josiah initially invests [tex]$360 in the account.
- The account earns 3% interest annually.
2. Identify the Formula for Compound Interest:
- The general formula for the amount \( y \) in an account with compound interest is:
\[
y = \text{principal} \times (1 + \text{interest rate})^x
\]
- In this formula:
- The principal is the initial amount of money deposited, which is $[/tex]360.
- The interest rate is the annual interest rate (converted from a percentage to a decimal), which is [tex]\( 3\% = 0.03 \)[/tex].
- The variable [tex]\( x \)[/tex] represents the number of years the money is invested.
3. Plug in the Values into the Formula:
- Using the values provided:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
4. Simplify the Formula:
- Calculate [tex]\( 1 + 0.03 \)[/tex]:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
- Substitute back into the equation:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
The equation that represents the amount in Josiah's account after [tex]\( x \)[/tex] years, with a 3% annual interest rate, is:
[tex]\[
y = 360(1.03)^x
\][/tex]
Therefore, the correct choice is [tex]\( y=360(1.03)^x \)[/tex].
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