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Answer :
Certainly! Let's work through the transactions to determine the recursive equation for Barry's account balance at the end of each month.
Barry performs these transactions each month:
1. Deposits [tex]$700.
2. Withdraws $[/tex]150 for gas.
3. Withdraws [tex]$400 for other expenses.
First, we need to figure out the net change to his account balance each month:
- The total withdrawal each month is $[/tex]150 + [tex]$400 = $[/tex]550.
- Since Barry deposits [tex]$700 every month, we calculate the net change by subtracting the total withdrawals from the deposit: $[/tex]700 - [tex]$550 = $[/tex]150.
This means each month, after all transactions, Barry's account balance increases by [tex]$150.
Based on this, we can set up the recursive formula:
- The initial balance at the end of the first month is $[/tex]1,900. So, we start with [tex]\( f(1) = 1,900 \)[/tex].
- Each subsequent month, his balance increases by $150, which gives us the recursive formula: [tex]\( f(n) = f(n-1) + 150 \)[/tex] for [tex]\( n \geq 2 \)[/tex].
Therefore, the correct choice is answer B:
[tex]\[ f(1) = 1,900 \][/tex]
[tex]\[ f(n) = f(n-1) + 150, \text{ for } n \geq 2 \][/tex]
Barry performs these transactions each month:
1. Deposits [tex]$700.
2. Withdraws $[/tex]150 for gas.
3. Withdraws [tex]$400 for other expenses.
First, we need to figure out the net change to his account balance each month:
- The total withdrawal each month is $[/tex]150 + [tex]$400 = $[/tex]550.
- Since Barry deposits [tex]$700 every month, we calculate the net change by subtracting the total withdrawals from the deposit: $[/tex]700 - [tex]$550 = $[/tex]150.
This means each month, after all transactions, Barry's account balance increases by [tex]$150.
Based on this, we can set up the recursive formula:
- The initial balance at the end of the first month is $[/tex]1,900. So, we start with [tex]\( f(1) = 1,900 \)[/tex].
- Each subsequent month, his balance increases by $150, which gives us the recursive formula: [tex]\( f(n) = f(n-1) + 150 \)[/tex] for [tex]\( n \geq 2 \)[/tex].
Therefore, the correct choice is answer B:
[tex]\[ f(1) = 1,900 \][/tex]
[tex]\[ f(n) = f(n-1) + 150, \text{ for } n \geq 2 \][/tex]
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