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.
104 exam-style questions on OCR A Level Maths 1.6 Exponentials and Logarithms, covering 1.6.1 Properties of the exponential function, 1.6.2 Gradient of e^(kx) (A-level only), 1.6.3 Definition of the logarithm, 1.6.4 The natural logarithm function, 1.6.5 ln x as inverse of e^x, 1.6.6 Laws of logarithms, 1.6.7 Equations involving exponentials, 1.6.8 Reduction to linear form, and 1.6.9 Modelling using exponential functions. Each one has a worked solution and a mark scheme showing where the marks go.