A telecommunications engineer is investigating the signal intensity, SSS (measured in picowatts), at a distance ddd (measured in metres) from a radio transmitter. The relationship is modelled by S=adbS = ad^bS=adb, where a a\,a and b b\,b are constants.
A graph shows a linear relationship between log10S\log_{10} Slog10S and log10d\log_{10} dlog10d. The line passes through the points (1,8)(1, 8)(1,8) and (4,2)(4, 2)(4,2).
Find an equation linking log10S\log_{10} Slog10S with log10d\log_{10} dlog10d.
Hence, or otherwise, express S S\,S in the form adbad^badb, where a a\,a and b b\,b are constants to be found.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.