Let's start by understanding the parameters provided:
- Josiah's initial investment is \$360.
- The account accrues interest at an annual rate of 3%.
When dealing with compound interest, the formula to determine the amount of money in the account after [tex]\( x \)[/tex] years is given by:
[tex]\[ y = P(1 + r)^x \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (the initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal).
- [tex]\( x \)[/tex] is the number of years.
- [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years.
Let's assign the given values to this formula:
- [tex]\( P = 360 \)[/tex]
- [tex]\( r = 0.03 \)[/tex] (since 3% as a decimal is 0.03)
- [tex]\( x \)[/tex] is the variable representing the number of years.
Plugging these values into the formula, we get:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying 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.
Among the given options, the correct equation is:
[tex]\[ y = 360(1.03)^x \][/tex]
So, the correct answer is:
[tex]\[ y = 360(1.03)^x \][/tex]
