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Answer :
To determine which recursive equation models Barry's account balance, let's break down his monthly transactions:
1. Deposits:
- Barry deposits [tex]$700 each month from his paycheck.
2. Withdrawals:
- He withdraws $[/tex]150 for gas.
- He also withdraws [tex]$400 for other expenses.
3. Net Monthly Change:
- The net effect on Barry's account each month can be calculated as:
\[
700 - 150 - 400 = 150
\]
- This means his account balance increases by $[/tex]150 each month.
Now, let's establish the recursive equation:
- At the end of the 1st month, Barry's account balance is [tex]$1,900. This is given as:
\[
f(1) = 1900
\]
- For subsequent months ($[/tex]n \geq 2[tex]$), the account balance can be found by adding the net monthly change ($[/tex]150) to the previous month's balance. Therefore, the recursive formula is:
[tex]\[
f(n) = f(n-1) + 150
\][/tex]
Comparing this with the provided options, this matches Option B:
- [tex]$f(1) = 1,900$[/tex]
- [tex]$f(n) = f(n-1) + 150$[/tex], for [tex]$n \geq 2$[/tex]
Therefore, the correct recursive equation is modeled by option B.
1. Deposits:
- Barry deposits [tex]$700 each month from his paycheck.
2. Withdrawals:
- He withdraws $[/tex]150 for gas.
- He also withdraws [tex]$400 for other expenses.
3. Net Monthly Change:
- The net effect on Barry's account each month can be calculated as:
\[
700 - 150 - 400 = 150
\]
- This means his account balance increases by $[/tex]150 each month.
Now, let's establish the recursive equation:
- At the end of the 1st month, Barry's account balance is [tex]$1,900. This is given as:
\[
f(1) = 1900
\]
- For subsequent months ($[/tex]n \geq 2[tex]$), the account balance can be found by adding the net monthly change ($[/tex]150) to the previous month's balance. Therefore, the recursive formula is:
[tex]\[
f(n) = f(n-1) + 150
\][/tex]
Comparing this with the provided options, this matches Option B:
- [tex]$f(1) = 1,900$[/tex]
- [tex]$f(n) = f(n-1) + 150$[/tex], for [tex]$n \geq 2$[/tex]
Therefore, the correct recursive equation is modeled by option B.
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