Answer :
To determine which recursive equation models Barry's account balance each month, let's take a closer look at the transactions and how they affect his balance.
Barry's monthly transactions are as follows:
- He deposits [tex]$700 into his account.
- He withdraws $[/tex]150 for gas.
- He withdraws [tex]$400 for other expenses.
Let's calculate the net change in Barry's account balance each month:
1. Deposits: Barry receives $[/tex]700.
2. Withdrawals: Barry loses [tex]$150 for gas and $[/tex]400 for other expenses, totaling [tex]$550 in withdrawals.
3. Net Change: The net change in his account balance per month is $[/tex]700 (deposit) minus [tex]$550 (total withdrawals), which equals a net increase of $[/tex]150.
Given this net change, we can now determine the recursive equation:
- His initial balance at the end of the 1st month is [tex]$1,900, as given.
- Each subsequent month's balance is the previous month's balance plus the net change of $[/tex]150.
Thus, the recursive equation that models Barry's account balance at the end of month [tex]\( n \)[/tex] is:
- [tex]\( f(1) = 1,900 \)[/tex]
- [tex]\( f(n) = f(n-1) + 150, \text{ for } n \geq 2 \)[/tex]
Looking at the answer choices, the correct option that matches this model is:
A.
[tex]\( f(1) = 1,900 \)[/tex]
[tex]\( f(n) = f(n-1) + 150, \text{ for } n \geq 2 \)[/tex]
Barry's monthly transactions are as follows:
- He deposits [tex]$700 into his account.
- He withdraws $[/tex]150 for gas.
- He withdraws [tex]$400 for other expenses.
Let's calculate the net change in Barry's account balance each month:
1. Deposits: Barry receives $[/tex]700.
2. Withdrawals: Barry loses [tex]$150 for gas and $[/tex]400 for other expenses, totaling [tex]$550 in withdrawals.
3. Net Change: The net change in his account balance per month is $[/tex]700 (deposit) minus [tex]$550 (total withdrawals), which equals a net increase of $[/tex]150.
Given this net change, we can now determine the recursive equation:
- His initial balance at the end of the 1st month is [tex]$1,900, as given.
- Each subsequent month's balance is the previous month's balance plus the net change of $[/tex]150.
Thus, the recursive equation that models Barry's account balance at the end of month [tex]\( n \)[/tex] is:
- [tex]\( f(1) = 1,900 \)[/tex]
- [tex]\( f(n) = f(n-1) + 150, \text{ for } n \geq 2 \)[/tex]
Looking at the answer choices, the correct option that matches this model is:
A.
[tex]\( f(1) = 1,900 \)[/tex]
[tex]\( f(n) = f(n-1) + 150, \text{ for } n \geq 2 \)[/tex]
