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Answer :
Sure! Let's solve this step by step:
When Josiah invests money, and the account earns interest annually, it's an example of compound interest. The formula for compound interest when interest is compounded annually is:
[tex]\[ y = P(1 + r)^x \][/tex]
Where:
- [tex]\( y \)[/tex] is the amount of money accumulated after [tex]\( x \)[/tex] years, including interest.
- [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 for.
In your problem:
- Josiah's initial investment [tex]\( P \)[/tex] is \$360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is equivalent to 0.03 in decimal form.
- We're looking for an equation that represents the amount [tex]\( y \)[/tex] after [tex]\( x \)[/tex] years.
Substitute the given values into the compound interest formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplify inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
So, the equation that represents the amount of money in the account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
That is the correct equation from the options given, which matches the choice:
[tex]\[ y = 360(1.03)^x \][/tex]
When Josiah invests money, and the account earns interest annually, it's an example of compound interest. The formula for compound interest when interest is compounded annually is:
[tex]\[ y = P(1 + r)^x \][/tex]
Where:
- [tex]\( y \)[/tex] is the amount of money accumulated after [tex]\( x \)[/tex] years, including interest.
- [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 for.
In your problem:
- Josiah's initial investment [tex]\( P \)[/tex] is \$360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is equivalent to 0.03 in decimal form.
- We're looking for an equation that represents the amount [tex]\( y \)[/tex] after [tex]\( x \)[/tex] years.
Substitute the given values into the compound interest formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplify inside the parentheses:
[tex]\[ y = 360(1.03)^x \][/tex]
So, the equation that represents the amount of money in the account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
That is the correct equation from the options given, which matches the choice:
[tex]\[ y = 360(1.03)^x \][/tex]
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