Select the correct answer.

Each month, Barry makes three transactions in his checking account:
- He deposits \$700 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 15th 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) = 150 \cdot f(n-1) \text{, for } n \geq 2[/tex]

B. [tex]f(1) = 1,900[/tex]
[tex]f(n) = f(n-1) + 700 \text{, for } n \geq 2[/tex]

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

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

Barry's checking account experiences three transactions each month:

1. A deposit of \[tex]$700.
2. A withdrawal of \$[/tex]150 for gas.
3. A withdrawal of \[tex]$400 for other expenses.

The net change in his account each month is calculated by adding the deposits and subtracting the withdrawals:

$[/tex][tex]$
\text{Net Change} = 700 - 150 - 400 = 150.
$[/tex][tex]$

This means that every month, Barry’s account balance increases by \$[/tex]150.

Given that the account balance at the end of the first month is \[tex]$1,900, the recursive equation representing the account balance at the end of month $[/tex]n[tex]$ is:

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

This corresponds to the recursive equation in choice D.