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Answer :
Certainly! Let's solve this step-by-step.
Josiah invests $360 into an account that accrues 3% interest annually. We need to find which equation represents the amount of money in Josiah's account, [tex]\( y \)[/tex], after [tex]\( x \)[/tex] years.
To solve this, we'll use the formula for compound interest, which is:
[tex]\[ y = P \times (1 + r)^x \][/tex]
where:
- [tex]\( P \)[/tex] is the initial investment (principal)
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal)
- [tex]\( x \)[/tex] is the number of years
- [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years
In this problem:
- [tex]\( P = 360 \)[/tex]
- [tex]\( r = 3\% = 0.03 \)[/tex]
Substitute these values into the formula:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
Simplify inside the parentheses:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
So, the 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]
From the given options:
1. [tex]\( y = 360(1.3)^x \)[/tex]
2. [tex]\( y = 360(0.3)^x \)[/tex]
3. [tex]\( y = 360(0.03)^x \)[/tex]
4. [tex]\( y = 360(1.03)^x \)[/tex]
The correct choice that matches our derived equation is:
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, the correct answer is the fourth option: [tex]\( y = 360(1.03)^x \)[/tex].
Josiah invests $360 into an account that accrues 3% interest annually. We need to find which equation represents the amount of money in Josiah's account, [tex]\( y \)[/tex], after [tex]\( x \)[/tex] years.
To solve this, we'll use the formula for compound interest, which is:
[tex]\[ y = P \times (1 + r)^x \][/tex]
where:
- [tex]\( P \)[/tex] is the initial investment (principal)
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal)
- [tex]\( x \)[/tex] is the number of years
- [tex]\( y \)[/tex] is the amount of money in the account after [tex]\( x \)[/tex] years
In this problem:
- [tex]\( P = 360 \)[/tex]
- [tex]\( r = 3\% = 0.03 \)[/tex]
Substitute these values into the formula:
[tex]\[ y = 360 \times (1 + 0.03)^x \][/tex]
Simplify inside the parentheses:
[tex]\[ y = 360 \times (1.03)^x \][/tex]
So, the 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]
From the given options:
1. [tex]\( y = 360(1.3)^x \)[/tex]
2. [tex]\( y = 360(0.3)^x \)[/tex]
3. [tex]\( y = 360(0.03)^x \)[/tex]
4. [tex]\( y = 360(1.03)^x \)[/tex]
The correct choice that matches our derived equation is:
[tex]\[ y = 360(1.03)^x \][/tex]
Therefore, the correct answer is the fourth option: [tex]\( y = 360(1.03)^x \)[/tex].
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