Answer :
Let's break down the situation with Barry's checking account to find the correct recursive equation.
Each month, Barry makes the following transactions:
1. Deposit from paycheck: [tex]$+700$[/tex]
2. Withdraw for gas: [tex]$-150$[/tex]
3. Withdraw for other expenses: [tex]$-400$[/tex]
To determine the net change in Barry’s account each month, we need to calculate the total impact of these transactions:
[tex]\[ \text{Net monthly change} = 700 - 150 - 400 \][/tex]
Let's do the math:
- [tex]$700 - 150 = 550$[/tex]
- [tex]$550 - 400 = 150$[/tex]
So, the net change in Barry's account each month is [tex]$+150$[/tex].
Now, let's look at the situation over time:
- Initial balance at the end of the 1st month: [tex]$1,900$[/tex]
Based on the transactions, Barry's balance increases by [tex]$150$[/tex] each month. Therefore, we can write the recursive equation as follows:
- Initial condition: [tex]\( f(1) = 1900 \)[/tex]
- Recursive formula for subsequent months (for [tex]\( n \geq 2 \)[/tex]): [tex]\( f(n) = f(n-1) + 150 \)[/tex]
This means each month Barry's account balance will increase by [tex]$150$[/tex] from the previous month's balance.
Given these steps, the correct answer is choice A:
[tex]\[ f(1) = 1900 \][/tex]
[tex]\[ f(n) = f(n-1) + 150 \quad \text{for} \, n \geq 2 \][/tex]
Each month, Barry makes the following transactions:
1. Deposit from paycheck: [tex]$+700$[/tex]
2. Withdraw for gas: [tex]$-150$[/tex]
3. Withdraw for other expenses: [tex]$-400$[/tex]
To determine the net change in Barry’s account each month, we need to calculate the total impact of these transactions:
[tex]\[ \text{Net monthly change} = 700 - 150 - 400 \][/tex]
Let's do the math:
- [tex]$700 - 150 = 550$[/tex]
- [tex]$550 - 400 = 150$[/tex]
So, the net change in Barry's account each month is [tex]$+150$[/tex].
Now, let's look at the situation over time:
- Initial balance at the end of the 1st month: [tex]$1,900$[/tex]
Based on the transactions, Barry's balance increases by [tex]$150$[/tex] each month. Therefore, we can write the recursive equation as follows:
- Initial condition: [tex]\( f(1) = 1900 \)[/tex]
- Recursive formula for subsequent months (for [tex]\( n \geq 2 \)[/tex]): [tex]\( f(n) = f(n-1) + 150 \)[/tex]
This means each month Barry's account balance will increase by [tex]$150$[/tex] from the previous month's balance.
Given these steps, the correct answer is choice A:
[tex]\[ f(1) = 1900 \][/tex]
[tex]\[ f(n) = f(n-1) + 150 \quad \text{for} \, n \geq 2 \][/tex]
