A solution containing hazardous waste is charged into a storage tank and subjected to a chemical treatment that decomposes the waste to harmless products. The concentration of the decomposing waste, C, has been reported to vary with time according to the formula C = 1 /(a + bt) when sufficient time has elapsed for the concentration to drop to 0.01g/L, the contents of the tank are discharged into a river that passes by the plant. The following data are taken for C and t:
(a) If the given formula is correct, what plot would yield a straight line that would enable you to determine the parameters a and b?
(b) Estimate a and b using the method of least squares (Appendix A.1). Check the goodness of fit by generating a plot of C versus t that shows both the measured and predicted values of C.
(c) Using the results of part (b), estimate the initial concentration of the waste in the tank and the time required for C to reach its discharge level.
(d) You should have very little confidence in the time estimated in part(c). Explain why.
(e) There are other potential problems with the whole waste disposal procedure. Suggest several of them.