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Answer :
To determine the correct equation that represents the amount of money in Josiah's account, [tex]\( y \)[/tex], after [tex]\( x \)[/tex] years, with an initial investment of \[tex]$360 and an annual interest rate of 3%, we need to use the formula for compound interest.
The formula for the amount of money \( y \) after \( x \) years with an initial principal \( P \) and an annual interest rate \( r \) is given by:
\[ y = P \times (1 + r)^x \]
Where:
- \( P \) is the initial investment (principal).
- \( r \) is the annual interest rate expressed as a decimal.
- \( x \) is the number of years.
- \( y \) is the amount of money in the account after \( x \) years.
In this problem:
- The initial investment \( P \) is \$[/tex]360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is 0.03 as a decimal.
Substituting the values into the formula, we get:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Therefore, the correct equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
So, the correct choice from the given options is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
The formula for the amount of money \( y \) after \( x \) years with an initial principal \( P \) and an annual interest rate \( r \) is given by:
\[ y = P \times (1 + r)^x \]
Where:
- \( P \) is the initial investment (principal).
- \( r \) is the annual interest rate expressed as a decimal.
- \( x \) is the number of years.
- \( y \) is the amount of money in the account after \( x \) years.
In this problem:
- The initial investment \( P \) is \$[/tex]360.
- The annual interest rate [tex]\( r \)[/tex] is 3%, which is 0.03 as a decimal.
Substituting the values into the formula, we get:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Therefore, the correct equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
So, the correct choice from the given options is:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
Thanks for taking the time to read Josiah invests tex 360 tex into an account that accrues tex 3 tex interest annually Assuming no deposits or withdrawals are made which equation represents. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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