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Answer :
To solve this problem, we need to determine which equation correctly represents the amount of money in Josiah's account after a certain number of years, given that the account accrues interest at a rate of 3% annually without any additional deposits or withdrawals.
Here’s a step-by-step guide to choosing the correct equation:
1. Understand Interest Accrual: Josiah's account is increasing by an annual interest rate of 3%. This means that each year, the amount in the account grows by 3% of the previous year's amount.
2. Initial Amount: Josiah initially invests \[tex]$360.
3. Interest Rate: The interest rate is 3%, which can also be expressed in decimal form as 0.03.
4. Compound Interest Formula: The formula to calculate the amount of money after compounding interest annually without additional deposits or withdrawals is:
\[
y = \text{principal} \times (1 + \text{interest rate})^x
\]
Here, \( y \) is the amount of money after \( x \) years, the principal is \$[/tex]360, and the interest rate in decimal form is 0.03.
5. Apply the Formula: Using the formula, we substitute the principal and interest rate:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
Simplifying [tex]\( (1 + 0.03) \)[/tex], we get:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
6. Select the Correct Option: Among the given options, the equation that matches this is:
- [tex]\( y = 360 \times (1.03)^x \)[/tex]
Therefore, the correct equation that represents the amount in Josiah's account after [tex]\( x \)[/tex] years is [tex]\( y = 360 \times (1.03)^x \)[/tex].
Here’s a step-by-step guide to choosing the correct equation:
1. Understand Interest Accrual: Josiah's account is increasing by an annual interest rate of 3%. This means that each year, the amount in the account grows by 3% of the previous year's amount.
2. Initial Amount: Josiah initially invests \[tex]$360.
3. Interest Rate: The interest rate is 3%, which can also be expressed in decimal form as 0.03.
4. Compound Interest Formula: The formula to calculate the amount of money after compounding interest annually without additional deposits or withdrawals is:
\[
y = \text{principal} \times (1 + \text{interest rate})^x
\]
Here, \( y \) is the amount of money after \( x \) years, the principal is \$[/tex]360, and the interest rate in decimal form is 0.03.
5. Apply the Formula: Using the formula, we substitute the principal and interest rate:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
Simplifying [tex]\( (1 + 0.03) \)[/tex], we get:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
6. Select the Correct Option: Among the given options, the equation that matches this is:
- [tex]\( y = 360 \times (1.03)^x \)[/tex]
Therefore, the correct equation that represents the amount in Josiah's account after [tex]\( x \)[/tex] years is [tex]\( y = 360 \times (1.03)^x \)[/tex].
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