Nana has a water purifier that filters \dfrac13 3 1 start fraction, 1, divided by, 3, end fraction of the contaminants each hour. She used it to purify water that had \dfrac12 2 1 start fraction, 1, divided by, 2, end fraction kilogram of contaminants. Write a function that gives the remaining amount of contaminants in kilograms, C(t)C(t)C, left parenthesis, t, right parenthesis, ttt hours after Nana started purifying the water.