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Answer :
Sure, let's go through the problem step by step.
Josiah invests \[tex]$360 into an account that accrues 3% interest annually. We need to find an equation that represents the amount of money in Josiah's account, \( y \), after \( x \) years.
### Step-by-Step Solution:
1. Initial Investment and Interest Rate:
- Initial investment = \$[/tex]360
- Annual interest rate = 3% (which is equivalent to 0.03 in decimal form)
2. Understanding Compound Interest:
- Interest compounds annually, so each year the amount of money in the account grows by a factor of [tex]\( 1 + \text{interest rate} \)[/tex].
3. Formulate the Equation:
- The amount of money after one year would be [tex]\( 360 \times (1 + 0.03) = 360 \times 1.03 \)[/tex].
- For two years, it would be [tex]\( 360 \times (1.03)^2 \)[/tex].
- Generally, after [tex]\( x \)[/tex] years, the amount [tex]\( y \)[/tex] can be represented by the formula:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
4. Matching with Given Options:
- We see that the equation [tex]\( y = 360 \times (1.03)^x \)[/tex] matches one of the provided options.
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 is:
[tex]\[ \boxed{y = 360(1.03)^x} \][/tex]
Josiah invests \[tex]$360 into an account that accrues 3% interest annually. We need to find an equation that represents the amount of money in Josiah's account, \( y \), after \( x \) years.
### Step-by-Step Solution:
1. Initial Investment and Interest Rate:
- Initial investment = \$[/tex]360
- Annual interest rate = 3% (which is equivalent to 0.03 in decimal form)
2. Understanding Compound Interest:
- Interest compounds annually, so each year the amount of money in the account grows by a factor of [tex]\( 1 + \text{interest rate} \)[/tex].
3. Formulate the Equation:
- The amount of money after one year would be [tex]\( 360 \times (1 + 0.03) = 360 \times 1.03 \)[/tex].
- For two years, it would be [tex]\( 360 \times (1.03)^2 \)[/tex].
- Generally, after [tex]\( x \)[/tex] years, the amount [tex]\( y \)[/tex] can be represented by the formula:
[tex]\[
y = 360 \times (1.03)^x
\][/tex]
4. Matching with Given Options:
- We see that the equation [tex]\( y = 360 \times (1.03)^x \)[/tex] matches one of the provided options.
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 is:
[tex]\[ \boxed{y = 360(1.03)^x} \][/tex]
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