Assignment:
A crude-oil refinery has an underground storage tank which has a fixed volume of 'V' liters. Due to pollutants, it gets contaminated with 'P(t)' kilograms of chemical waste at time 't' which is evenly distributed throughout the tank.
Oil containing a variety of pollutants with concentration of 'k' kilograms per liter enters the tank at a rate of 'R' liters per minute, and the completely mixed solution leaves at the same rate.
a) If 'P0' is the amount of pollutants in the tank at time t=0 then find 'P(t)' for any time t.
b) If k=0, find the time 'T' for the waste to be reduced to 40% of its original value.
Provide complete and step by step solution for the question and show calculations and use formulas.