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 A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.