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Answer :
To determine which equation represents the amount of money in Josiah's account after a number of years, let's break down the problem.
Josiah invests $360 into an account that accrues interest at an annual rate of 3%. The interest is compounded annually, meaning the amount of interest earned each year is added to the principal to calculate interest for the following year.
The general formula for compound interest is:
[tex]\[ y = P(1 + r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the total amount after [tex]\( x \)[/tex] years,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal),
- [tex]\( x \)[/tex] is the number of years.
Let's substitute the known values into the formula:
- [tex]\( P = 360 \)[/tex]
- [tex]\( r = 0.03 \)[/tex] (3% as a decimal)
Putting these values into the compound interest equation, we get:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying the equation inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, 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]
This matches the option: [tex]\( y = 360(1.03)^x \)[/tex].
Josiah invests $360 into an account that accrues interest at an annual rate of 3%. The interest is compounded annually, meaning the amount of interest earned each year is added to the principal to calculate interest for the following year.
The general formula for compound interest is:
[tex]\[ y = P(1 + r)^x \][/tex]
where:
- [tex]\( y \)[/tex] is the total amount after [tex]\( x \)[/tex] years,
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal),
- [tex]\( x \)[/tex] is the number of years.
Let's substitute the known values into the formula:
- [tex]\( P = 360 \)[/tex]
- [tex]\( r = 0.03 \)[/tex] (3% as a decimal)
Putting these values into the compound interest equation, we get:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplifying the equation inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, 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]
This matches the option: [tex]\( y = 360(1.03)^x \)[/tex].
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