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Answer :
Sure! Let's walk through how to find the equation that represents the amount of money in Josiah's account after a certain number of years with an interest rate.
Josiah invests [tex]$360 into an account with an annual interest rate of 3%. This is a case of compound interest, which means the interest is applied to the total amount in the account each year, not just the initial amount.
The formula to calculate compound interest is:
\[ y = P(1 + r)^x \]
Where:
- \( y \) is the amount of money in the account after \( x \) years.
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (expressed as a decimal).
- \( x \) is the number of years the money is invested.
For this problem:
- The principal \( P \) is $[/tex]360.
- The interest rate [tex]\( r \)[/tex] is 3% per year, which as a decimal is 0.03.
- [tex]\( x \)[/tex] represents the number of years.
Substitute these values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplify the expression inside the parenthesis:
[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]
This equation reflects how his investment grows each year due to the compound interest.
Josiah invests [tex]$360 into an account with an annual interest rate of 3%. This is a case of compound interest, which means the interest is applied to the total amount in the account each year, not just the initial amount.
The formula to calculate compound interest is:
\[ y = P(1 + r)^x \]
Where:
- \( y \) is the amount of money in the account after \( x \) years.
- \( P \) is the principal amount (initial investment).
- \( r \) is the annual interest rate (expressed as a decimal).
- \( x \) is the number of years the money is invested.
For this problem:
- The principal \( P \) is $[/tex]360.
- The interest rate [tex]\( r \)[/tex] is 3% per year, which as a decimal is 0.03.
- [tex]\( x \)[/tex] represents the number of years.
Substitute these values into the formula:
[tex]\[ y = 360(1 + 0.03)^x \][/tex]
Simplify the expression inside the parenthesis:
[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]
This equation reflects how his investment grows each year due to the compound interest.
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