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Answer :
To solve the problem of determining which equation best represents the amount of money in Josiah's account after [tex]$x$[/tex] years, we need to use the formula for compound interest. Here are the steps:
1. Identify Initial Investment and Interest Rate:
- Josiah initially invests [tex]$360.
- The account accrues interest at a rate of 3% per year.
2. Understand the Compound Interest Formula:
The formula for compound interest, which calculates the amount of money accumulated after a certain number of years, including interest, is:
\[
y = P(1 + r)^x
\]
where:
- \( y \) is the final amount of money.
- \( P \) is the initial principal balance (here, $[/tex]360).
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal). For 3%, [tex]\( r = 0.03 \)[/tex].
- [tex]\( x \)[/tex] is the number of years the money is invested or borrowed.
3. Plug Values into the Formula:
Substitute the known values into the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Simplify the Equation:
Simplify inside the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So the equation becomes:
[tex]\[
y = 360(1.03)^x
\][/tex]
This equation, [tex]\( y = 360(1.03)^x \)[/tex], correctly represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years. Therefore, the correct choice from the given options is:
- [tex]\( y = 360(1.03)^x \)[/tex]
1. Identify Initial Investment and Interest Rate:
- Josiah initially invests [tex]$360.
- The account accrues interest at a rate of 3% per year.
2. Understand the Compound Interest Formula:
The formula for compound interest, which calculates the amount of money accumulated after a certain number of years, including interest, is:
\[
y = P(1 + r)^x
\]
where:
- \( y \) is the final amount of money.
- \( P \) is the initial principal balance (here, $[/tex]360).
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal). For 3%, [tex]\( r = 0.03 \)[/tex].
- [tex]\( x \)[/tex] is the number of years the money is invested or borrowed.
3. Plug Values into the Formula:
Substitute the known values into the formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
4. Simplify the Equation:
Simplify inside the parentheses:
[tex]\[
1 + 0.03 = 1.03
\][/tex]
So the equation becomes:
[tex]\[
y = 360(1.03)^x
\][/tex]
This equation, [tex]\( y = 360(1.03)^x \)[/tex], correctly represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years. Therefore, the correct choice from the given options is:
- [tex]\( y = 360(1.03)^x \)[/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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