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.
