A stream traverses two lakes flowing downstream, and carrying fresh water as it enters the upper lake. The upper lake contains 4∗109 gallons of water, and the lower lake contains 2 ∗109 gallons of water. The flow rate of the stream is the same at all points and is 4 ∗ 106 gallons per day. A factory situated at the upper lake releases a pollutant at a rate of 200 lbs. per day. Let Q1(t) and Q2(t) be the amount, in pounds, of pollutant in the upper and lower lakes, respectively, where time t is measured in days. Assuming that each lake is well mixed, Q1 and Q2 obey the system(a) Q'1 = 4 ∗ 106 (200 − Q1), Q'2 = 4 ∗ 106 (Q1 − Q2).(b) Q'1 = 200 − Q1/1000, Q'2 = Q1/1000 − Q2/500.(c) Q'1 = 200 − 4 ∗ 106Q1, Q'2 = 4 ∗ 106 (Q1 − Q2).
(d) Q'1 = 200t − 4 ∗ 106Q1, Q'2 = 4 ∗ 106 (Q1 − Q2).