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Answer :
To solve this problem, we need to find the correct equation representing the amount of money in Josiah's account after accruing interest. Josiah invests [tex]$360 in an account with an annual interest rate of 3%.
The formula for calculating the amount of money in an account with compound interest over time is:
\[ y = P(1 + r)^x \]
Where:
- \( y \) is the amount of money in the account after \( x \) years.
- \( P \) is the principal amount (initial investment), which is $[/tex]360.
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal), which is 3%, or 0.03.
- [tex]\( x \)[/tex] is the number of years the money is invested for.
Substitute the given values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Now, simplify the expression inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years. So, the correct option is:
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, the right answer is [tex]\( y = 360(1.03)^x \)[/tex].
The formula for calculating the amount of money in an account with compound interest over time is:
\[ y = P(1 + r)^x \]
Where:
- \( y \) is the amount of money in the account after \( x \) years.
- \( P \) is the principal amount (initial investment), which is $[/tex]360.
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal), which is 3%, or 0.03.
- [tex]\( x \)[/tex] is the number of years the money is invested for.
Substitute the given values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Now, simplify the expression inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years. So, the correct option is:
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, the right answer is [tex]\( y = 360(1.03)^x \)[/tex].
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