We appreciate your visit to Select the correct answer Each month Barry makes three transactions in his checking account He deposits tex 700 tex from his paycheck He withdraws tex. 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 the problem of finding the recursive equation that models Barry's account balance at the end of each month, let's break down his transactions step-by-step.
1. Initial Balance:
- At the end of the 1st month, Barry has a balance of [tex]$1,900 in his checking account. So, we start with:
\[
f(1) = 1,900
\]
2. Monthly Transactions:
- Each month, Barry makes the following transactions:
- He deposits $[/tex]700 from his paycheck.
- He withdraws [tex]$150 to buy gas.
- He withdraws $[/tex]400 for other expenses.
3. Net Change in Balance Each Month:
- To determine the effect of these transactions on his account balance, we calculate the net change as follows:
[tex]\[
\text{Net Change} = \text{Deposits} - (\text{Withdrawals for Gas} + \text{Withdrawals for Other Expenses})
\][/tex]
[tex]\[
\text{Net Change} = 700 - (150 + 400)
\][/tex]
[tex]\[
\text{Net Change} = 700 - 550 = 150
\][/tex]
4. Forming the Recursive Equation:
- Now that we know the net change per month is $150, we can form a recursive equation to model Barry's account balance at the end of each month:
- At month [tex]\( n \)[/tex], the balance is the previous month's balance plus the net change:
[tex]\[
f(n) = f(n-1) + 150, \text{ for } n \geq 2
\][/tex]
5. Selecting the Correct Option:
- Based on the steps above, we conclude that the recursive equation matching these conditions is:
- [tex]\( f(1) = 1,900 \)[/tex]
- [tex]\( f(n) = f(n-1) + 150, \text{ for } n \geq 2 \)[/tex]
This matches option A, which is the correct answer.
1. Initial Balance:
- At the end of the 1st month, Barry has a balance of [tex]$1,900 in his checking account. So, we start with:
\[
f(1) = 1,900
\]
2. Monthly Transactions:
- Each month, Barry makes the following transactions:
- He deposits $[/tex]700 from his paycheck.
- He withdraws [tex]$150 to buy gas.
- He withdraws $[/tex]400 for other expenses.
3. Net Change in Balance Each Month:
- To determine the effect of these transactions on his account balance, we calculate the net change as follows:
[tex]\[
\text{Net Change} = \text{Deposits} - (\text{Withdrawals for Gas} + \text{Withdrawals for Other Expenses})
\][/tex]
[tex]\[
\text{Net Change} = 700 - (150 + 400)
\][/tex]
[tex]\[
\text{Net Change} = 700 - 550 = 150
\][/tex]
4. Forming the Recursive Equation:
- Now that we know the net change per month is $150, we can form a recursive equation to model Barry's account balance at the end of each month:
- At month [tex]\( n \)[/tex], the balance is the previous month's balance plus the net change:
[tex]\[
f(n) = f(n-1) + 150, \text{ for } n \geq 2
\][/tex]
5. Selecting the Correct Option:
- Based on the steps above, we conclude that the recursive equation matching these conditions is:
- [tex]\( f(1) = 1,900 \)[/tex]
- [tex]\( f(n) = f(n-1) + 150, \text{ for } n \geq 2 \)[/tex]
This matches option A, which is the correct answer.
Thanks for taking the time to read Select the correct answer Each month Barry makes three transactions in his checking account He deposits tex 700 tex from his paycheck He withdraws tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
