Cyanide is used in solution to isolate gold in a mine. This may result in contaminated groundwater near the mine, requiring the poison be removed, as in the following table, where t is in years since 2012. 

(a) Find an exponential model for c(t), the concentration, in parts per million, of cyanide in the groundwater.

(b) Use the model in part (a) to find the number of years it takes for the cyanide concentration to fall to 10 ppm. 

(c) The filtering process removing the cyanide is sped up so that the new model is D(t) = c(2t). Find D(t).

(d) If the cyanide removal was started three years earlier, but run at the speed of part (a), find a new model, E(t).

t (years) c(t) (ppm) 0 1 25.0 21.8 2 19.01