Math 166 Project
Pollution

One of the earliest pollution problems brought to the attention of the Environmental Protection Agency (EPA) was the case of Sioux Lake in eastern South Dakota.  For years a small paper plant located nearby had been discharging waste containing carbon tetrachloride (CCL4) into the waters of the lake.  The EPA ordered the installation of filters designed to slow and eventually stop the flow of CCL4 from the mill.  At the time the EPA learned of the problem the pollutant was being discharged at a rate of 16 cubic yards/year.  Implementation of this program took exactly 3 years during which time the flow of pollutant remained almost steady.  Once the filters were installed, the flow declined.  The following data was obtained during a 10 year period.  Time t=0 corresponds to the time the EPA learned of the problem and the rate is given in cubic yards per year.
________________________________________________________________ 
t     0    1     2    3      4     5    6     7    8    9    10   

rate 16  15.9  16.1  16.05  9.15  3.95 1.11 .009 .005 .001 .0005
________________________________________________________________ 

a.  Use the ListPlot command to draw a graph of the rate of CCL4 flow into the lake as a function of time beginning at the time the EPA first learned of the problem.  Label your axes.

b.  Use all the data and a right Riemann sum to estimate the amount of CCL4 which entered the water during the 10 years.  Give the correct units of your answer.

c.  Use all the data and a left Riemann sum to estimate the amount of CCL4 which entered the water during the 10 years. Give the correct units of your answer.


It was observed that the flow of the pollutant can be approximately modeled by the continuous function

            16   for   0 æ t æ3
  r(t)=     t2-14t+49  for  3 æ t æ 7
            0  for  t Ñ 7,
where r(t) is given in cubic yards per year.

Use this function to answer the following questions.

d.  Draw a graph showing the rate, r(t), of CCL4 flow into the lake as a function of time beginning at the time the EPA first learned of the situation.  Use the Show command to plot this graph and your data from (a) on the same plot.

e.  How much CCL4 entered the waters during these 7 years?

f.  What was the average rate of flow of CCL4 during the first seven years; i.e., the time which elapsed between when the EPA learned of the situation and the time the pollution flow essentially stopped?