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Answer :
To solve this question, we need to determine which equation represents the amount of money in Josiah's account after a certain number of years, given that he invests [tex]$360 at an annual interest rate of 3%.
Here's how you can solve it step-by-step:
1. Understand the problem: Josiah invests $[/tex]360, and the account accrues 3% interest annually. We need an equation that shows how much money, [tex]\(y\)[/tex], will be in the account after [tex]\(x\)[/tex] years.
2. Identify the formula: The appropriate formula for calculating the balance in an account with compound interest is:
[tex]\[
A = P(1 + r)^n
\][/tex]
where:
- [tex]\(A\)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\(P\)[/tex] is the principal amount (initial investment) which is $360.
- [tex]\(r\)[/tex] is the annual interest rate (in decimal form), so 3% becomes 0.03.
- [tex]\(n\)[/tex] is the number of years.
3. Plug in the values: Substitute the given values into the formula:
[tex]\[
A = 360(1 + 0.03)^x
\][/tex]
Simplifying inside the parentheses gives:
[tex]\[
A = 360(1.03)^x
\][/tex]
4. Select the correct equation: From the options provided, [tex]\(y = 360(1.03)^x\)[/tex] is the equation that matches the derived formula for the accumulated amount.
Therefore, the correct equation that represents the amount of money in Josiah's account after [tex]\(x\)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
Here's how you can solve it step-by-step:
1. Understand the problem: Josiah invests $[/tex]360, and the account accrues 3% interest annually. We need an equation that shows how much money, [tex]\(y\)[/tex], will be in the account after [tex]\(x\)[/tex] years.
2. Identify the formula: The appropriate formula for calculating the balance in an account with compound interest is:
[tex]\[
A = P(1 + r)^n
\][/tex]
where:
- [tex]\(A\)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\(P\)[/tex] is the principal amount (initial investment) which is $360.
- [tex]\(r\)[/tex] is the annual interest rate (in decimal form), so 3% becomes 0.03.
- [tex]\(n\)[/tex] is the number of years.
3. Plug in the values: Substitute the given values into the formula:
[tex]\[
A = 360(1 + 0.03)^x
\][/tex]
Simplifying inside the parentheses gives:
[tex]\[
A = 360(1.03)^x
\][/tex]
4. Select the correct equation: From the options provided, [tex]\(y = 360(1.03)^x\)[/tex] is the equation that matches the derived formula for the accumulated amount.
Therefore, the correct equation that represents the amount of money in Josiah's account after [tex]\(x\)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
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