An environmental scientist monitors the concentration, C C\,C parts per million (ppm), of a specific chemical pollutant in a reservoir over time t t\,t months. The scientist identifies a linear relationship between log10C\log_{10} Clog10C and ttt. The line representing this relationship passes through the points (2.4,1.82)(2.4, 1.82)(2.4,1.82) and (6.4,0.42)(6.4, 0.42)(6.4,0.42).
Determine the equation for the relationship between log10C\log_{10} Clog10C and ttt.
Hence, or otherwise, express C C\,C in the form kbtkb^tkbt, giving the values of the constants k k\,k and b b\,b to 3 significant figures.