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]\$ 150[/tex] to buy gas for his car.
- He withdraws [tex]\$ 400[/tex] for other expenses.

If his account balance is [tex]\$ 1,900[/tex] at the end of the 1st month, which recursive equation models Barry's account balance at the end of month [tex]n[/tex]?

A. [tex]f(1) = 1,900[/tex]
[tex]f(n) = f(n-1) + 700 - 150 - 400[/tex], for [tex]n \geq 2[/tex]

B. [tex]f(1) = 1,900[/tex]
[tex]f(n) = 150 \cdot f(n-1)[/tex], for [tex]n \geq 2[/tex]

C. [tex]f(1) = 1,900[/tex]
[tex]f(n) = f(n-1) - 150[/tex], for [tex]n \geq 2[/tex]

D. [tex]f(1) = 1,900[/tex]
[tex]f(n) = f(n-1) + 150[/tex], for [tex]n \geq 2[/tex]

Barry's account balance at the end of the first month is given as

[tex]$$
f(1) = 1900.
$$[/tex]

Each month, he makes three transactions:

1. He deposits \[tex]$700.
2. He withdraws \$[/tex]150 for gas.
3. He withdraws \[tex]$400 for other expenses.

The net change in his account each month is

$[/tex][tex]$
700 - 150 - 400 = 150.
$[/tex][tex]$

This means that starting from month 2, his balance increases by \$[/tex]150 each month. Therefore, the recursive equation that models his account balance is

[tex]$$
f(1)=1900, \quad f(n)=f(n-1)+150 \text{ for } n\geq 2.
$$[/tex]

This corresponds to option D.

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!

Rewritten by : Barada

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