We have recently suggested that dust growth in the cold gas phase dominates the dust abundance in elliptical galaxies while dust is efficiently destroyed in the hot X-ray emitting plasma (hot gas). In order to understand the dust evolution in elliptical galaxies, we construct a simple model that includes dust growth in the cold gas and dust destruction in the hot gas. We also take into account the effect of mass exchange between these two gas components induced by active galactic nucleus (AGN) feedback. We survey reasonable ranges of the relevant parameters in the model and find that AGN feedback cycles actually produce a variety in cold gas mass and dust-to-gas ratio. By comparing with an observational sample of nearby elliptical galaxies, we find that, although the dust-to-gas ratio varies by an order of magnitude in our model, the entire range of the observed dust-to-gas ratios is difficult to be reproduced under a single parameter set. Variation of the dust growth efficiency is the most probable solution to explain the large variety in dust-to-gas ratio of the observational sample. Therefore, dust growth can play a central role in creating the variation in dust-to-gas ratio through the AGN feedback cycle and through the variation in dust growth efficiency.
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