The initial concentration of phosphorous (C) in a waste water pond is 107 ppm, as against the acceptable limit of 6.75x10 ppm. The concentration (C) will reduce as fresh water enters the pond. The differential equation that governs the concentration, C as a function of time (in weeks) is given by. dC + 0.06 C = 0, C (0) 107 ppm dt Using Euler's method and a step size of 3.5 weeks, Calculate (1.) The concentration of the phosphorus after 7 weeks. (H.) Exact concentration after 7 weeks (i.) Relative absolute error

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The initial concentration of phosphorous (C) in a waste water pond is 107 ppm, as against
the acceptable limit of 6.75x10 ppm. The concentration (C) will reduce as fresh water enters
the pond. The differential equation that governs the concentration, C as a function of time (in
weeks) is given by,
dC
+0.06 C = 0, C (0) =107 ppm
dt
Using Euler's method and a step size of 3.5 weeks,
Calculate
(1.)
The concentration of the phosphorus after 7 weeks.
(.)
Exact concentration after 7 weeks
(.)
Relative absolute error
Transcribed Image Text:The initial concentration of phosphorous (C) in a waste water pond is 107 ppm, as against the acceptable limit of 6.75x10 ppm. The concentration (C) will reduce as fresh water enters the pond. The differential equation that governs the concentration, C as a function of time (in weeks) is given by, dC +0.06 C = 0, C (0) =107 ppm dt Using Euler's method and a step size of 3.5 weeks, Calculate (1.) The concentration of the phosphorus after 7 weeks. (.) Exact concentration after 7 weeks (.) Relative absolute error
de
+ 0.06 C =0
de
-o.0の C
h= 3.5
to = 0
t=35
t2 = 7
CCt.) = CCto)+
%3D
メ3-5
dC cC3-s) = C (6) + × 3:5 H C4。っC-)
%3D
C(3-5) = 10
- 0.06 (10) x 3-5
CC35)- 0799 メ10t
PPm
%3D
de l.
C t2) = C(ti)+
JE'tい c1
X 3.S
9.0のへo 49 メット)×3.5
SCE)
624 メ10 PPm
%3D
Transcribed Image Text:de + 0.06 C =0 de -o.0の C h= 3.5 to = 0 t=35 t2 = 7 CCt.) = CCto)+ %3D メ3-5 dC cC3-s) = C (6) + × 3:5 H C4。っC-) %3D C(3-5) = 10 - 0.06 (10) x 3-5 CC35)- 0799 メ10t PPm %3D de l. C t2) = C(ti)+ JE'tい c1 X 3.S 9.0のへo 49 メット)×3.5 SCE) 624 メ10 PPm %3D
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