A standard dishwasher in our home removes particulates and grease from dishware at a rate of approximately 8% per minute when using a commercially available detergent. This removal process has been...

A standard dishwasher in our home removes particulates and grease from dishware at a rate of approximately 8% per minute when using a commercially available detergent. This removal process has been shown to follow first-order reaction kinetics. In your efforts to conserve water, you decide not to prewash your dishes and to cut your dishwasher's wash cycle (typically equal to 27 minutes) in half (i.e., you're planning to run the dishwasher on the wash cycle only for 13.5 minutes). What is the resulting concentration of "dirt" on your dishes [g per dish] under these conditions if your average dish has 0.78 g of dirt initially? What is the concentration of "dirt" in the wash water [mg/L] under these conditions if your wash cycle uses 4 gallons of water on average?