Comet 49P/Arend-Rigaux is a well known low-activity Jupiter Family comet. Despite the low activity, we have witnessed outgassing activity in 1992, 2004, and 2012. In 2012 a broad tail-like feature (PA$sim270^circ, sim2.3times10^5$ km) and a narrow jet-like feature (PA$sim180^circ, sim9.3times10^4$ km) were seen simultaneously. Using Finson-Probstein (FP) dust dynamical models we determine: grain sizes released in each event; duration of activity; when activity peaked; and velocity of the dust particles, allowing us to make comparisons between the events. We find that the tail feature in 2012 is similar to the tail in 1992 with large grains (40-4000 $mu$m) peaking in activity near perihelion with a long outgassing duration greater than 150 days. The jet feature from 2012, however, is more similar to the 2004 event which we model with small grains (1-8 $mu$m) with a short duration of activity ($sim$1 month). The main difference between these two features is that the 2004 event occurs prior to perihelion, while the 2012 event is post-perihelion. We use the grain sizes from the FP models to constrain ice sublimation models. Between 1985 and 2018 we cover 6 apparitions with 26 nights of our own observations plus data from the literature and the Minor Planet Center, which together, allow us to model the heliocentric light curve. We find that the models are consistent with H$_2$O ice sublimation as the volatile responsible for driving activity over most of the active phases and a combination of H$_2$O and CO$_2$ ices are responsible for driving activity near perihelion. We measure the fractional active area over time for H$_2$O and discover that the activity decreases from an average active area of $sim3%$ to $sim0.2%$. This secular decrease in activity implies that the comet is becoming depleted of volatiles and is in the process of transitioning to a dormant or dead state.
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