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.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 100 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.