A researcher is investigating the relationship between the intensity of light, y y\,y lux, and the distance, x x\,x m, from a laser source.
She finds that the plot of log10y\log_{10} ylog10y against log10x\log_{10} xlog10x is a straight line passing through the points (1, 7)(1,\ 7)(1, 7) and (4, 1)(4,\ 1)(4, 1).
Determine an equation linking log10y\log_{10} ylog10y with log10x\log_{10} xlog10x.
Hence express y y\,y in the form pxqpx^{q}pxq, where p p\,p and q q\,q are constants to be found.
The researcher claims that the intensity of the light is inversely proportional to the square of the distance from the source. Explain how your answer to part (b) supports this claim.