Community Garden Water Management

You volunteer at a local community garden that serves families from diverse backgrounds. The garden has a 200-gallon water storage tank that collects rainwater and receives treated water from the city. Your job is to monitor the water quality by tracking the concentration of nutrients that are added to help the plants grow.

Initially, the tank contains 200 gallons of water with [latex]3[/latex] pounds of dissolved nutrients. At [latex]t = 0[/latex] (measured in hours), the garden begins receiving city water that flows into the tank at a rate of [latex]5[/latex] gallons per hour. This incoming water contains nutrients at a concentration of [latex]0.2[/latex] pounds per gallon. To maintain proper circulation, water flows out of the tank at the same rate of [latex]5[/latex] gallons per hour, keeping the volume constant at 200 gallons. The water in the tank is continuously mixed by a solar-powered pump.

Later in the day, you also need to monitor the temperature of water in a small greenhouse pool used for starting seedlings. The pool water needs to cool from its daytime temperature to be suitable for sensitive plants overnight.