Question

As a member of Engineers Without Borders, you are working in a community that has contaminated drinking water caused by slow growing bacteria introduced to the cistern from surface water runoff. The water is safe to drink when the concentration of bacteria is below 475#/1000mL. A disinfectant must be added to the community cistern (after every rainfall) when the bacteria level reaches 475# /1000mL in order to make the water safe for human consumption. (The disinfectant is not effective for levels below 475# /1000mL). You take the following measurements after a recent rainfall: t (hours) c (#/1000mL) 10 370 7 354 6 348 3 4 5 340 1 2 364 360 320 330 280 305 1. Fit a power model to the data and find the following: best-fit equation (transformed and untransformed) b. plot the data and the model (transformed and untransformed) total sum of the squares, St sum of the squares of the residuals, S standard error, S y/x correlation coefficient, g. coefficient of determination, r h. predict the bacteria concentration at 12 hours after the rainfall. a. C. d. e. f. r 2. Fit an exponential model to the data and find the following: a. best-fit equation (transformed and untransformed) b. plot the data and the model (transformed and untransformed) c. total sum of the squares, St d. sum of the squares of the residuals, Sr e. standard error, Sy/x f. correlation coefficient, r g. coefficient of determination, r2 h. predict the bacteria concentration at 12 hours after the rainfall. 3. Based on problems 1-2 which model best describes the data. Justify and explain your answer. The disinfectant cannot be added until the bacteria concentration reaches 475#/1000ML. Use the best model to calculate the time at which the disinfectant must be added to the cistern in order for the water to be safe for consumption.
just answer part 3

Answer 1

Since the coefficient of determination (r²) is more for the power model (1) than the exponential model (.905) we say that the power model fits the data the best.

The power model is given as y^= a* x^b = 280.184 * x^.12

For bacteria concentration to reach 475/1000mL,the time taken by power model is given as 475 = 280.184 * x^.12

Then x= 81.36 = 81 hours (app)