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Answer :
To determine which equation represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years with an annual interest rate of [tex]\( 3\% \)[/tex], starting with an initial investment of \$360, we can break down the process of calculating compound interest.
1. Identify the principal amount (initial investment):
- [tex]\( P = 360 \)[/tex]
2. Identify the annual interest rate:
- The interest rate is [tex]\( 3\% \)[/tex]. In decimal form, this is [tex]\( 0.03 \)[/tex].
3. Understand the compound interest formula:
- The formula for compound interest when interest is compounded annually is:
[tex]\[
y = P \times (1 + r)^x
\][/tex]
where:
- [tex]\( y \)[/tex] is the amount of money after [tex]\( x \)[/tex] years,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( x \)[/tex] is the number of years.
4. Substitute the known values into the formula:
- Substitute [tex]\( P = 360 \)[/tex] and [tex]\( r = 0.03 \)[/tex] into the formula:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
5. Simplify the expression:
- Simplifying inside the parentheses gives:
[tex]\[
y = 360 \times 1.03^x
\][/tex]
So, 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]
This matches the option:
- [tex]\( y = 360(1.03)^x \)[/tex]
1. Identify the principal amount (initial investment):
- [tex]\( P = 360 \)[/tex]
2. Identify the annual interest rate:
- The interest rate is [tex]\( 3\% \)[/tex]. In decimal form, this is [tex]\( 0.03 \)[/tex].
3. Understand the compound interest formula:
- The formula for compound interest when interest is compounded annually is:
[tex]\[
y = P \times (1 + r)^x
\][/tex]
where:
- [tex]\( y \)[/tex] is the amount of money after [tex]\( x \)[/tex] years,
- [tex]\( P \)[/tex] is the principal amount,
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal),
- [tex]\( x \)[/tex] is the number of years.
4. Substitute the known values into the formula:
- Substitute [tex]\( P = 360 \)[/tex] and [tex]\( r = 0.03 \)[/tex] into the formula:
[tex]\[
y = 360 \times (1 + 0.03)^x
\][/tex]
5. Simplify the expression:
- Simplifying inside the parentheses gives:
[tex]\[
y = 360 \times 1.03^x
\][/tex]
So, 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]
This matches the option:
- [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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