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.
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.