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Answer :
To find the equation representing the amount of money in Josiah's account after accruing interest, we use the formula for compound interest. Here's the step-by-step process:
1. Understand the Problem: Josiah invests $360 in an account with an annual interest rate of 3%. We want to find the amount, [tex]\( y \)[/tex], in the account after [tex]\( x \)[/tex] years, with no additional deposits or withdrawals.
2. Identify the Compound Interest Formula:
[tex]\[
y = P(1 + r)^x
\][/tex]
where:
- [tex]\( P \)[/tex] is the initial principal (the starting amount),
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form),
- [tex]\( x \)[/tex] is the number of years.
3. Assign Values to the Variables:
- The initial principal [tex]\( P = 360 \)[/tex].
- The annual interest rate is 3%, which as a decimal is [tex]\( r = 0.03 \)[/tex].
- [tex]\( x \)[/tex] is the number of years.
4. Plug the Values into the Formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Equation:
- Calculate [tex]\( 1 + 0.03 = 1.03 \)[/tex].
6. Final Equation:
- The expression for the amount of money in the account after [tex]\( x \)[/tex] years is:
[tex]\[
y = 360(1.03)^x
\][/tex]
From the choices provided, 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].
1. Understand the Problem: Josiah invests $360 in an account with an annual interest rate of 3%. We want to find the amount, [tex]\( y \)[/tex], in the account after [tex]\( x \)[/tex] years, with no additional deposits or withdrawals.
2. Identify the Compound Interest Formula:
[tex]\[
y = P(1 + r)^x
\][/tex]
where:
- [tex]\( P \)[/tex] is the initial principal (the starting amount),
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form),
- [tex]\( x \)[/tex] is the number of years.
3. Assign Values to the Variables:
- The initial principal [tex]\( P = 360 \)[/tex].
- The annual interest rate is 3%, which as a decimal is [tex]\( r = 0.03 \)[/tex].
- [tex]\( x \)[/tex] is the number of years.
4. Plug the Values into the Formula:
[tex]\[
y = 360(1 + 0.03)^x
\][/tex]
5. Simplify the Equation:
- Calculate [tex]\( 1 + 0.03 = 1.03 \)[/tex].
6. Final Equation:
- The expression for the amount of money in the account after [tex]\( x \)[/tex] years is:
[tex]\[
y = 360(1.03)^x
\][/tex]
From the choices provided, 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].
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