2. A lake contains 1010 litres of water. Acid rain containing 0.02 milligrams of pollutant per litre of rain falls into the lake at a rate of 103 litres per week. An outlet stream drains away 103 litres of water per week. Assume that the pollutant is always evenly distributed throughout the lake, so the runoff into the stream has the same concentration of pollutant as the lake as a whole. The volume of the lake stays constant at 1010 litres because the water lost from the runoff balances exactly the water gained from the rain. (a) Write a differential equation whose solution is P(t), the number of milligrams of pollutant in the lake as a function of t measured in weeks. (b) Find any equilibrium solutions. (c) Sketch some representative solution curves. (d) How would you alter the differential equation if there was a dry spell and rain was falling into the lake at a rate of only 102 litres per week