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L1592_frame_C40 Page 362 Tuesday, December 18, 2001 3:24 PM

Exercises
40.1 PCB Degradation in Soil. PCB-contaminated sewage sludge was applied to test plots at three
different loading rates (kg/ha) at the beginning of a 5-yr experimental program. Test plots of
farmland where corn was grown were sampled to assess the rate of disappearance of PCB
from soil. Duplicate plots were used for each treatment. Soil PCB concentration (mg/kg) was
measured each year in the fall after the corn crop was picked and in the spring before planting.
The data are below. Estimate the rate coefficients of disappearance (k) using the model PCB t =
PCB 0 exp(−kt). Are the rates the same for the four treatment conditions?

Time Treatment 1 Treatment 2 Treatment 3
0 1.14 0.61 2.66 2.50 0.44 0.44
5 0.63 0.81 2.69 2.96 0.25 0.31
12 0.43 0.54 1.14 1.51 0.18 0.22
17 0.35 0.51 1.00 0.48 0.15 0.12
24 0.35 0.34 0.93 1.16 0.11 0.09
29 0.32 0.30 0.73 0.96 0.08 0.10
36 0.23 0.20 0.47 0.46 0.07 0.06
41 0.20 0.16 0.57 0.36 0.03 0.04
48 0.12 0.09 0.40 0.22 0.03 0.03
53 0.11 0.08 0.32 0.31 0.02 0.03

40.2 1,1,1-Trichloroethane Biodegradation. Estimates of biodegradation rate (k b ) of 1,1,1-trichlo-
roethane were made under three conditions of activated sludge treatment. The model is y i =
bx i + e i , where the slope b is the estimate of k b . Two dummy variables are needed to represent
the three treatment conditions, and these are arranged in the table below. Does the value of
k b depend on the activated sludge treatment condition?

−− − −6 ∗∗ ∗ ∗ ∗∗ ∗ ∗ −− − −3
x (×× ××10 ) Z 1 Z 2 Z 1 x Z 2 x y(×× ××10 )
61.2 0 0 0 0 142.3
9.8 0 0 0 0 140.8
8.9 0 0 0 0 62.7
44.9 0 0 0 0 32.5
6.3 0 0 0 0 82.3
20.3 0 0 0 0 58.6
7.5 0 0 0 0 15.5
1.2 0 0 0 0 2.5
159.8 1 0 159.8 0 1527.3
44.4 1 0 44.4 0 697.5
57.4 1 0 57.4 0 429.9
25.9 1 0 25.9 0 215.2
37.9 1 0 37.9 0 331.6
55.0 1 0 55.0 0 185.7
151.7 1 0 151.7 0 1169.2
116.2 1 0 116.2 0 842.8
129.9 1 0 129.9 0 712.9
19.4 0 1 0 19.4 49.3
7.7 0 1 0 7.7 21.6
36.7 0 1 0 36.7 53.3
17.8 0 1 0 17.8 59.4
8.5 0 1 0 8.5 112.3

© 2002 By CRC Press LLC