Answer :
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.
[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.