Cyanide is used in solution to isolate gold in a mine.¹ This may result in contaminated groundwater near the mine, which needs to be filetered. The following table gives the concentration, c(t) (in parts per million), of cyanide in the groundwater, where t is in years since 2017. 1 www.waterboards.ca.gov, accessed September 16, 2019. t (years) c(t) (ppm) 25.0 21.8 19.01 (a) Find an exponential model for c(t). 0 i 1 (b) Use the model in part (a) to find the number of years it takes for the cyanide concentration to fall to 11 ppm. Round to three decimal places. 2 (c) The filtering process removing the cyanide is sped up so that the new model is D(t) = c(2t). Find D(t). 1.c (t) = 25(0.872)', D (t) = 25(0.7604)', E (t) = 16.576(0.872)' II. c (t) = 16.576(0.872)', D (t) = 25(0.7604)', E (t) = 25(0.872)' (d) If the cyanide removal was started three years earlier, but run at the speed of part (a), find a new model, E(t). III. c (t) = 16.576(0.7604)', D (t) = 25(0.7604)', E (t) = 25(0.872)' IV. c'(t) = 16.576(0.7604)', D (t) = 16.576(0.872)', E (t) = 25(0.872)'

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