In order to keep a malfunctioning satellite from falling into the earth, space agency officials decide to use a powerful rocket. At the time the rocket is attached, the satellite will be traveling with an initial velocity,
v
0
v
0

v, start subscript, 0, end subscript, and for every second that the rocket fires, it will add approximately
180
180180 meters per second
(
m
s
)
(
s
m

)left parenthesis, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction, right parenthesis to this velocity. In order to ensure safety on earth, the velocity must be increased to at least
3
,
800

m
s
3,800
s
m

3, comma, 800, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction . Also, the rocket can fire for no more than
4
44 seconds. For the initial velocity of the satellite,
v
0
v
0

v, start subscript, 0, end subscript, which of the following systems of inequalities best models this situation, where
t
tt is time, in seconds, after the rocket is first fired?