Scenario: Years of overusing fertilizers have caused soil in a farming area to become acidic, with a chemical contamination level of 2000 mg/kg of dry soil. A slurry reactor experiment is conducted to remove the contaminants. Details of the experiment setup: Soil gathered: 4 kg Reactor setup: 12 kg of soil per m³ of slurry Soil-water partition coefficient: 0.42 m³/kg Biodegradation rate constant: 0.2 day?¹ Soil density: 2600 kg/m³ Goal: Reduce the concentration to 50 mg/kg of dry soil Duration: 100 days, under equilibrium conditions Questions: a. Derive the governing differential equation for the liquid phase concentration over time. b. Solve this equation analytically for the liquid phase concentration as a function of time. c. Create a plot of liquid-phase concentration vs. time in Excel. d. Check if 100 days is enough for remediation or calculate the minimum time required manually.