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Answer :
Certainly! Let's determine the correct equation for the amount of money in Josiah's account after a certain number of years.
1. Principal Amount:
- Josiah invests [tex]$360 initially. This is the principal amount (P).
2. Interest Rate:
- The account earns 3% interest annually. To use it in calculations, we convert this percentage into a decimal: 3% becomes 0.03.
3. Compound Interest Formula:
- The formula to calculate the amount of money in an account with compound interest is:
\[
y = P(1 + r)^x
\]
where:
- \( y \) is the future value of the investment,
- \( P \) is the principal amount ($[/tex]360 in this case),
- [tex]\( r \)[/tex] is the annual interest rate in decimal form (0.03),
- [tex]\( x \)[/tex] is the number of years the money is invested.
4. Substitute the values:
- Based on what we know, plug the numbers into the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
- Simplifying inside the parentheses gives:
[tex]\[
y = 360(1.03)^x
\][/tex]
The correct equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
So the correct option from the choices is [tex]\( y = 360(1.03)^x \)[/tex].
1. Principal Amount:
- Josiah invests [tex]$360 initially. This is the principal amount (P).
2. Interest Rate:
- The account earns 3% interest annually. To use it in calculations, we convert this percentage into a decimal: 3% becomes 0.03.
3. Compound Interest Formula:
- The formula to calculate the amount of money in an account with compound interest is:
\[
y = P(1 + r)^x
\]
where:
- \( y \) is the future value of the investment,
- \( P \) is the principal amount ($[/tex]360 in this case),
- [tex]\( r \)[/tex] is the annual interest rate in decimal form (0.03),
- [tex]\( x \)[/tex] is the number of years the money is invested.
4. Substitute the values:
- Based on what we know, plug the numbers into the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
- Simplifying inside the parentheses gives:
[tex]\[
y = 360(1.03)^x
\][/tex]
The correct equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
So the correct option from the choices is [tex]\( y = 360(1.03)^x \)[/tex].
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