Most accretion disc models consider the accretion rate to be steady and nonvarying or run disk simulations with one accretion rate at a time to determine how the different rates affect disk dynamics.However, in the case of a black hole accreting from its companion star, the accretion rate should progressively vary since the star may still be evolving and because of additional mass that is loss via the stellar winds.In order to investigate how a varying accretion rate in the context of spiral density waves effect the dynamics of the disc: I use the recently made public code, Fargo3d,to simulate the effects of a varying accretion rate and compare them with a simulation of a consistent accretion rate.Three different accretion rates, one of which was constant, were supplied to magnetized thin disks with an aspect ratio of 0.1.The results indicate that there is indeed a difference between a constant accretion rate and a varying one as both of the disks with the varying accretion rates produced more turbulence over time, i.e.a high value of alpha(the turbulent velocity over the sound speed), than the constant accretion rate.It is also worth noting that the accretion rate with the least total mass of the three had a greater value than the constant accretion rate.This may have great implications in the way we view disk models as the assumption of a constant accretion rate may not be as inconsequential as proposed.