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Allow the baking soda paste to sit on the plastic for 20 to 30 minutes. The baking soda will loosen the dirt on the plastic. Remove the remaining paste by rinsing the plastic thoroughly with clean water. This should rinse away any dirt or grime the paste loosened.  Smaller items can be placed in the sink to be rinsed. A large item can be rinsed with a garden hose.
Let the paste sit on the plastic. Rinse the plastic. Dry the plastic with a towel, or sit it out to air dry.