An engineer is modelling the signal strength, S S\,S microvolts, of a transmitter at a distance of x x\,x km from it.
A plot of log10S\log_{10} Slog10S against x x\,x produces a straight line lll.
The line l l\,l passes through the points (0, 3.42)(0,\ 3.42)(0, 3.42) and (12, 1.02)(12,\ 1.02)(12, 1.02).
Find an equation for lll.
Hence express S S\,S in the form kbxkb^{x}kbx, giving the value of k k\,k and the value of b b\,b to 3 significant figures.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.