We appreciate your visit to Each month Barry makes three transactions in his checking account He deposits tex 700 tex from his paycheck He withdraws tex 150 tex to buy. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To solve this problem, let's break down Barry's transactions and see how they affect his account balance each month.
Each month, Barry:
1. Deposits [tex]$700 into his account.
2. Withdraws $[/tex]150 for gas.
3. Withdraws [tex]$400 for other expenses.
To find the net change in his account balance each month, we can calculate it by looking at the total deposits and withdrawals:
- Total deposits = $[/tex]700
- Total withdrawals = [tex]$150 (gas) + $[/tex]400 (expenses) = [tex]$550
The net change in the balance each month is therefore:
\[ \text{Net change} = 700 - 550 = 150 \]
Barry's account balance at the end of the first month is $[/tex]1,900. From the second month onward, the balance changes by [tex]$150 each month. We can express this situation as a recursive equation:
1. The initial condition is that at the end of the first month, his balance is $[/tex]1,900:
[tex]\[ f(1) = 1,900 \][/tex]
2. For any month [tex]\( n \geq 2 \)[/tex], the account balance is the previous month's balance plus the net change of [tex]$150:
\[ f(n) = f(n-1) + 150 \]
Therefore, the recursive equation that models Barry's account balance at the end of month \( n \) is:
C. \( f(1) = 1,900 \)
\( f(n) = f(n-1) + 150 \), for \( n \geq 2 \)
This equation accounts for the monthly deposit and withdrawals, reflecting the net increase of $[/tex]150 each month.
Each month, Barry:
1. Deposits [tex]$700 into his account.
2. Withdraws $[/tex]150 for gas.
3. Withdraws [tex]$400 for other expenses.
To find the net change in his account balance each month, we can calculate it by looking at the total deposits and withdrawals:
- Total deposits = $[/tex]700
- Total withdrawals = [tex]$150 (gas) + $[/tex]400 (expenses) = [tex]$550
The net change in the balance each month is therefore:
\[ \text{Net change} = 700 - 550 = 150 \]
Barry's account balance at the end of the first month is $[/tex]1,900. From the second month onward, the balance changes by [tex]$150 each month. We can express this situation as a recursive equation:
1. The initial condition is that at the end of the first month, his balance is $[/tex]1,900:
[tex]\[ f(1) = 1,900 \][/tex]
2. For any month [tex]\( n \geq 2 \)[/tex], the account balance is the previous month's balance plus the net change of [tex]$150:
\[ f(n) = f(n-1) + 150 \]
Therefore, the recursive equation that models Barry's account balance at the end of month \( n \) is:
C. \( f(1) = 1,900 \)
\( f(n) = f(n-1) + 150 \), for \( n \geq 2 \)
This equation accounts for the monthly deposit and withdrawals, reflecting the net increase of $[/tex]150 each month.
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