Answer :
Let's solve the problem step by step to determine the correct recursive equation for Barry's account balance.
1. Understand the Transactions:
- Barry deposits \[tex]$700 each month from his paycheck.
- He withdraws \$[/tex]150 for gas each month.
- He withdraws \[tex]$400 for other expenses each month.
2. Calculate the Net Change Each Month:
- The total amount Barry withdraws each month is \$[/tex]150 (gas) + \[tex]$400 (expenses) = \$[/tex]550.
- The difference between his deposit and his withdrawals is \[tex]$700 (deposit) - \$[/tex]550 (total withdrawals) = \[tex]$150.
3. Initial Condition:
- At the end of the 1st month, Barry's account balance is given as \$[/tex]1,900.
4. Recursive Equation:
- Since each month, Barry's balance increases by the net change amount, the recursive equation can be written as:
- [tex]\( f(1) = 1,900 \)[/tex]
- [tex]\( f(n) = f(n-1) + 150 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
Therefore, the correct answer is option B:
[tex]\( f(1) = 1,900 \)[/tex]
[tex]\( f(n) = f(n-1) + 150 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
1. Understand the Transactions:
- Barry deposits \[tex]$700 each month from his paycheck.
- He withdraws \$[/tex]150 for gas each month.
- He withdraws \[tex]$400 for other expenses each month.
2. Calculate the Net Change Each Month:
- The total amount Barry withdraws each month is \$[/tex]150 (gas) + \[tex]$400 (expenses) = \$[/tex]550.
- The difference between his deposit and his withdrawals is \[tex]$700 (deposit) - \$[/tex]550 (total withdrawals) = \[tex]$150.
3. Initial Condition:
- At the end of the 1st month, Barry's account balance is given as \$[/tex]1,900.
4. Recursive Equation:
- Since each month, Barry's balance increases by the net change amount, the recursive equation can be written as:
- [tex]\( f(1) = 1,900 \)[/tex]
- [tex]\( f(n) = f(n-1) + 150 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
Therefore, the correct answer is option B:
[tex]\( f(1) = 1,900 \)[/tex]
[tex]\( f(n) = f(n-1) + 150 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
