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Answer :
To determine the equation that represents the amount of money in Josiah's account after a certain number of years, we need to use the formula for compound interest. The formula is:
[tex]\[ y = P(1 + r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the principal amount (the initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form).
- [tex]\( x \)[/tex] is the time in years.
In this problem:
- Josiah's initial investment, [tex]\( P \)[/tex], is \$360.
- The annual interest rate, [tex]\( r \)[/tex], is 3%, which is 0.03 in decimal form.
- We are looking for the equation that represents [tex]\( y \)[/tex] after [tex]\( x \)[/tex] years.
Substituting the given values into the formula, we have:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
This matches the option: [tex]\( y=360(1.03)^x \)[/tex].
[tex]\[ y = P(1 + r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years.
- [tex]\( P \)[/tex] is the principal amount (the initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form).
- [tex]\( x \)[/tex] is the time in years.
In this problem:
- Josiah's initial investment, [tex]\( P \)[/tex], is \$360.
- The annual interest rate, [tex]\( r \)[/tex], is 3%, which is 0.03 in decimal form.
- We are looking for the equation that represents [tex]\( y \)[/tex] after [tex]\( x \)[/tex] years.
Substituting the given values into the formula, we have:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
This matches the option: [tex]\( y=360(1.03)^x \)[/tex].
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