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Ecoli_Leastsquares_Example

# Ecoli_Leastsquares_Example - Example of Curve Fitting Using...

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Example of Curve Fitting Using Least Squares Prof. Dragan Djurdjanovic ME 218 Fall 2008

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The Problem The concentration of E. coli bacteria in a swimming area is monitored for hygiene purposes. It is measured in what are called CFU’s or “colony forming units ”. After a heavy rain shower, the no. of CFUs shows a drastic increase due to bacteria being washed down by the rain. The swimming area is continuously monitored before deeming it fit for use. Before a rain shower After a rain shower
Given Data The following data is given for the concentration of E. coli in a particular swimming area after a storm Time (hrs) 4 8 12 16 20 24 Conc (CFU per 100 ml) 1590 1320 1000 900 650 560 NOTE: 1. Bacteria concentration always decreases with time 2. Negative concentration is impossible

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Choice of model Given the data, and the two important points, we assume that the concentration of bacteria decreases exponentially with time (t), or C = C 0 exp(-t/k) where, C = concentration after time t hrs C 0 = initial concentration, i.e., immediately after the storm k = time constant
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