The light intensity, III lux, measured after passing through nnn layers of a specific optical filter, is modelled by the relationship I=abnI = ab^nI=abn where aaa and bbb are constants. Experimental data for the first 5 layers is used to plot a graph of log10I\log_{10} Ilog10I against nnn. The data points are found to lie on a straight line with a gradient of −0.11-0.11−0.11 and a vertical intercept of 2.452.452.45 on the log10I\log_{10} Ilog10I axis.
Determine the value of aaa and the value of bbb according to the model, rounding your answers to two decimal places.
Provide a practical interpretation of the constant aaa in the context of this model.
Use the model to estimate the light intensity when 8 layers of the filter are used.
