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Answer :
To solve the problem of determining which equation represents the amount of money in Josiah's account after [tex]$x$[/tex] years, we need to use the concept of compound interest.
Josiah's investment grows with compound interest, where the formula is:
[tex]\[ y = P \times (1 + r)^x \][/tex]
where:
- [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 the money is invested.
In this question:
- The principal amount [tex]\( P \)[/tex] is \$360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which as a decimal is 0.03.
- The number of years is represented by [tex]\( x \)[/tex].
So, substituting these values into the compound interest formula, we get:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Therefore, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Among the given options, this matches the fourth equation:
[tex]\[ y = 360(1.03)^x \][/tex]
This is the correct choice.
Josiah's investment grows with compound interest, where the formula is:
[tex]\[ y = P \times (1 + r)^x \][/tex]
where:
- [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 the money is invested.
In this question:
- The principal amount [tex]\( P \)[/tex] is \$360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which as a decimal is 0.03.
- The number of years is represented by [tex]\( x \)[/tex].
So, substituting these values into the compound interest formula, we get:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Therefore, the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Among the given options, this matches the fourth equation:
[tex]\[ y = 360(1.03)^x \][/tex]
This is the correct choice.
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