A beekeeper's initial observation of the population of a certain bee colony was $1,800$ bees. The beekeeper set a goal to increase the population to $3,300$ bees. The beekeeper uses a model that predicts the population of this bee colony begins at $1,800$ and increases by $120$ bees per week in the first two weeks after the initial observation, and then increases by $180$ bees per week until the beekeeper's goal is reached. According to this model, at the end of week $w$ after the initial observation, where $w > 2$, which of the following functions gives the predicted number of bees still needed to reach the beekeeper's goal?