We appreciate your visit to Each month Barry makes three transactions in his checking account He deposits tex 700 tex from his paycheck He withdraws tex 150 tex to buy. 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 solve this problem and find the correct recursive equation for Barry's account balance, let's carefully look at his transaction pattern each month.
1. Understand the initial account balance:
- Barry starts with an account balance of \[tex]$1,900 at the end of the 1st month. This is defined as \( f(1) = 1,900 \).
2. Calculate the net change in his account per month:
- He deposits \$[/tex]700 from his paycheck.
- He withdraws \[tex]$150 for gas.
- He withdraws \$[/tex]400 for other expenses.
3. Determine the total monthly change:
- Total monthly change = Deposit from paycheck - Withdraw for gas - Withdraw for expenses
- Total monthly change = \[tex]$700 - \$[/tex]150 - \[tex]$400 = \$[/tex]150
4. Formulate the recursive equation:
- The balance at the end of each month depends on the balance at the end of the previous month, plus the monthly net change.
- Therefore, the recursive equation for Barry's account balance at the end of month [tex]\( n \)[/tex] is:
[tex]\[
f(n) = f(n-1) + 150, \text{ for } n \geq 2
\][/tex]
Given the above steps, the correct option is:
C.
[tex]\( f(1) = 1,900 \)[/tex]
[tex]\( f(n) = f(n-1) + 150, \text{ for } n \geq 2 \)[/tex]
1. Understand the initial account balance:
- Barry starts with an account balance of \[tex]$1,900 at the end of the 1st month. This is defined as \( f(1) = 1,900 \).
2. Calculate the net change in his account per month:
- He deposits \$[/tex]700 from his paycheck.
- He withdraws \[tex]$150 for gas.
- He withdraws \$[/tex]400 for other expenses.
3. Determine the total monthly change:
- Total monthly change = Deposit from paycheck - Withdraw for gas - Withdraw for expenses
- Total monthly change = \[tex]$700 - \$[/tex]150 - \[tex]$400 = \$[/tex]150
4. Formulate the recursive equation:
- The balance at the end of each month depends on the balance at the end of the previous month, plus the monthly net change.
- Therefore, the recursive equation for Barry's account balance at the end of month [tex]\( n \)[/tex] is:
[tex]\[
f(n) = f(n-1) + 150, \text{ for } n \geq 2
\][/tex]
Given the above steps, the correct option is:
C.
[tex]\( f(1) = 1,900 \)[/tex]
[tex]\( f(n) = f(n-1) + 150, \text{ for } n \geq 2 \)[/tex]
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