Answer :
Let's work through the problem step by step to find the correct recursive equation that models Barry's account balance.
1. Understanding Barry's transactions:
- Each month, Barry deposits [tex]$700 from his paycheck into his checking account.
- He withdraws $[/tex]150 for gas.
- He also withdraws [tex]$400 for other expenses.
- The total amount withdrawn each month is $[/tex]150 + [tex]$400 = $[/tex]550.
2. Calculate the net change in the account per month:
- Deposit: [tex]$700
- Total withdrawals: $[/tex]550
- Net change per month = Deposit - Withdrawals = [tex]$700 - $[/tex]550 = [tex]$150
3. Initial condition:
- At the end of the first month, Barry's account balance is $[/tex]1,900.
4. Modeling the account balance with a recursive equation:
- We are given several options to choose from. We want to find the equation that correctly represents the situation.
Let's evaluate the relevant option:
- Option A. [tex]\( f(1) = 1,900 \)[/tex]
- Recursive formula: [tex]\( f(n) = f(n-1) + 150 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
This option starts with an initial balance of [tex]$1,900, which matches Barry's balance at the end of the first month. The recursive formula adds $[/tex]150 per month, which accurately reflects the net change in Barry's account.
Therefore, the correct recursive equation that models Barry's account balance is option A.
1. Understanding Barry's transactions:
- Each month, Barry deposits [tex]$700 from his paycheck into his checking account.
- He withdraws $[/tex]150 for gas.
- He also withdraws [tex]$400 for other expenses.
- The total amount withdrawn each month is $[/tex]150 + [tex]$400 = $[/tex]550.
2. Calculate the net change in the account per month:
- Deposit: [tex]$700
- Total withdrawals: $[/tex]550
- Net change per month = Deposit - Withdrawals = [tex]$700 - $[/tex]550 = [tex]$150
3. Initial condition:
- At the end of the first month, Barry's account balance is $[/tex]1,900.
4. Modeling the account balance with a recursive equation:
- We are given several options to choose from. We want to find the equation that correctly represents the situation.
Let's evaluate the relevant option:
- Option A. [tex]\( f(1) = 1,900 \)[/tex]
- Recursive formula: [tex]\( f(n) = f(n-1) + 150 \)[/tex], for [tex]\( n \geq 2 \)[/tex]
This option starts with an initial balance of [tex]$1,900, which matches Barry's balance at the end of the first month. The recursive formula adds $[/tex]150 per month, which accurately reflects the net change in Barry's account.
Therefore, the correct recursive equation that models Barry's account balance is option A.
