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.
104 exam-style questions on OCR (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.