Answer :
To solve this problem, let's examine Barry's monthly transactions:
1. Barry deposits [tex]$700 from his paycheck into his account each month.
2. He withdraws $[/tex]150 to buy gas.
3. He withdraws [tex]$400 for other expenses.
To find the net change to his account each month, we calculate the difference between the deposits and withdrawals:
- Total deposit: $[/tex]700
- Total withdrawals: [tex]$150 (for gas) + $[/tex]400 (for other expenses) = [tex]$550
The net change to his account balance each month is:
\[ \text{Net change} = \text{Total deposit} - \text{Total withdrawals} \]
\[ \text{Net change} = 700 - 550 = 150 \]
This tells us that Barry's account balance will increase by $[/tex]150 each month after all transactions.
Given that the account balance at the end of the 1st month is $1,900, we can use this information to model the recursive equation for his account balance at the end of month [tex]\( n \)[/tex]:
- Start with the balance at the end of the 1st month: [tex]\( f(1) = 1,900 \)[/tex]
- For each subsequent month, use the recursive relationship:
[tex]\[ f(n) = f(n-1) + 150 \][/tex]
where [tex]\( n \geq 2 \)[/tex].
The correct recursive model for Barry's account balance is:
- [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 A.
1. Barry deposits [tex]$700 from his paycheck into his account each month.
2. He withdraws $[/tex]150 to buy gas.
3. He withdraws [tex]$400 for other expenses.
To find the net change to his account each month, we calculate the difference between the deposits and withdrawals:
- Total deposit: $[/tex]700
- Total withdrawals: [tex]$150 (for gas) + $[/tex]400 (for other expenses) = [tex]$550
The net change to his account balance each month is:
\[ \text{Net change} = \text{Total deposit} - \text{Total withdrawals} \]
\[ \text{Net change} = 700 - 550 = 150 \]
This tells us that Barry's account balance will increase by $[/tex]150 each month after all transactions.
Given that the account balance at the end of the 1st month is $1,900, we can use this information to model the recursive equation for his account balance at the end of month [tex]\( n \)[/tex]:
- Start with the balance at the end of the 1st month: [tex]\( f(1) = 1,900 \)[/tex]
- For each subsequent month, use the recursive relationship:
[tex]\[ f(n) = f(n-1) + 150 \][/tex]
where [tex]\( n \geq 2 \)[/tex].
The correct recursive model for Barry's account balance is:
- [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 A.
