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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 understand how compound interest works.
1. Initial Investment and Interest Rate:
- Josiah starts with an initial investment of $360.
- The annual interest rate is 3%, which in decimal form is 0.03.
2. Compound Interest Formula:
- The general formula for compound interest is:
[tex]\[
y = P(1 + r)^x
\][/tex]
- Here, [tex]\( P \)[/tex] is the principal amount (initial investment), [tex]\( r \)[/tex] is the annual interest rate in decimal form, and [tex]\( x \)[/tex] is the number of years.
3. Applying the Values Given:
- Substitute the principal [tex]\( P = 360 \)[/tex] and the interest rate [tex]\( r = 0.03 \)[/tex] into the compound interest formula. Therefore, the equation becomes:
[tex]\[
y = 360 (1 + 0.03)^x
\][/tex]
- Simplify inside the parenthesis:
[tex]\[
y = 360 (1.03)^x
\][/tex]
4. Choosing the Correct Option:
- Look at the options provided:
- [tex]\( y=360(1.3)^x \)[/tex]
- [tex]\( y=360(0.3)^x \)[/tex]
- [tex]\( y=360(0.03)^x \)[/tex]
- [tex]\( y=360(1.03)^x \)[/tex]
- The correct representation of the amount of money after [tex]\( x \)[/tex] years, with the 3% interest applied annually, is:
[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].
1. Initial Investment and Interest Rate:
- Josiah starts with an initial investment of $360.
- The annual interest rate is 3%, which in decimal form is 0.03.
2. Compound Interest Formula:
- The general formula for compound interest is:
[tex]\[
y = P(1 + r)^x
\][/tex]
- Here, [tex]\( P \)[/tex] is the principal amount (initial investment), [tex]\( r \)[/tex] is the annual interest rate in decimal form, and [tex]\( x \)[/tex] is the number of years.
3. Applying the Values Given:
- Substitute the principal [tex]\( P = 360 \)[/tex] and the interest rate [tex]\( r = 0.03 \)[/tex] into the compound interest formula. Therefore, the equation becomes:
[tex]\[
y = 360 (1 + 0.03)^x
\][/tex]
- Simplify inside the parenthesis:
[tex]\[
y = 360 (1.03)^x
\][/tex]
4. Choosing the Correct Option:
- Look at the options provided:
- [tex]\( y=360(1.3)^x \)[/tex]
- [tex]\( y=360(0.3)^x \)[/tex]
- [tex]\( y=360(0.03)^x \)[/tex]
- [tex]\( y=360(1.03)^x \)[/tex]
- The correct representation of the amount of money after [tex]\( x \)[/tex] years, with the 3% interest applied annually, is:
[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].
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