A telecommunications engineer is modeling the signal strength, SSS microvolts, of a transmitter at a distance xxx km. A plot of log10S\log_{10} Slog10S against xxx produces a straight line lll.
The line lll passes through the points (0,3.42)(0, 3.42)(0,3.42) and (12,1.02)(12, 1.02)(12,1.02).
Write down an equation for lll.
Hence, or otherwise, express SSS in the form kbxkb^xkbx, giving the values of the constants kkk and bbb 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.