We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To find the equation that represents the amount of money in Josiah's account after a certain number of years, we need to use the formula for compound interest. The compound interest formula is:
[tex]\[ A = P(1 + r)^x \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( x \)[/tex] years, including interest.
- [tex]\( P \)[/tex] is the principal amount (initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal).
- [tex]\( x \)[/tex] is the number of years the money is invested for.
For Josiah's investment:
- The initial investment [tex]\( P \)[/tex] is $360.
- The interest rate [tex]\( r \)[/tex] is 3%, which we convert to a decimal by dividing by 100. So, [tex]\( r = 0.03 \)[/tex].
- The number of years is represented by [tex]\( x \)[/tex].
Plugging these values into the formula gives:
[tex]\[ A = 360(1 + 0.03)^x \][/tex]
Simplifying inside the parentheses:
[tex]\[ A = 360(1.03)^x \][/tex]
So the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
This matches the choice: [tex]\( y = 360(1.03)^x \)[/tex].
[tex]\[ A = P(1 + r)^x \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( x \)[/tex] years, including interest.
- [tex]\( P \)[/tex] is the principal amount (initial investment).
- [tex]\( r \)[/tex] is the annual interest rate (as a decimal).
- [tex]\( x \)[/tex] is the number of years the money is invested for.
For Josiah's investment:
- The initial investment [tex]\( P \)[/tex] is $360.
- The interest rate [tex]\( r \)[/tex] is 3%, which we convert to a decimal by dividing by 100. So, [tex]\( r = 0.03 \)[/tex].
- The number of years is represented by [tex]\( x \)[/tex].
Plugging these values into the formula gives:
[tex]\[ A = 360(1 + 0.03)^x \][/tex]
Simplifying inside the parentheses:
[tex]\[ A = 360(1.03)^x \][/tex]
So the equation that represents the amount of money in Josiah's account after [tex]\( x \)[/tex] years is:
[tex]\[ y = 360(1.03)^x \][/tex]
This matches the choice: [tex]\( y = 360(1.03)^x \)[/tex].
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