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Answer :
To solve this problem, we are working with compound interest. Josiah invests [tex]$360 at an annual interest rate of 3%. We need to find the equation that represents the amount of money, \( y \), in Josiah's account after \( x \) years.
The formula for calculating compound interest is:
\[ A = P(1 + r)^t \]
Where:
- \( A \) is the amount of money after \( t \) years.
- \( P \) is the principal amount, which is \$[/tex]360 in this case.
- [tex]\( r \)[/tex] is the annual interest rate. Here, it is 3%, which in decimal form is 0.03.
- [tex]\( t \)[/tex] is the time in years.
We want to represent this in terms of [tex]\( y \)[/tex] for Josiah's account:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying the expression, we combine [tex]\( 1 + 0.03 \)[/tex] to get 1.03. Thus, the equation becomes:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation shows that the amount in the account grows at a rate of 1.03 times each year due to the interest. So, the correct answer that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
The formula for calculating compound interest is:
\[ A = P(1 + r)^t \]
Where:
- \( A \) is the amount of money after \( t \) years.
- \( P \) is the principal amount, which is \$[/tex]360 in this case.
- [tex]\( r \)[/tex] is the annual interest rate. Here, it is 3%, which in decimal form is 0.03.
- [tex]\( t \)[/tex] is the time in years.
We want to represent this in terms of [tex]\( y \)[/tex] for Josiah's account:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying the expression, we combine [tex]\( 1 + 0.03 \)[/tex] to get 1.03. Thus, the equation becomes:
[tex]\[ y = 360(1.03)^x \][/tex]
This equation shows that the amount in the account grows at a rate of 1.03 times each year due to the interest. So, the correct answer that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
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