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 (MEI) A Level Maths 1.8 Exponentials and Logarithms, covering 1.8.1 The function y = a^x, 1.8.2 Convert between index and logarithmic form, 1.8.3 Logarithm as inverse of exponential, 1.8.4 Laws of logarithms, 1.8.5 Values of log_a a and log_a 1, 1.8.6 Solve equations of the form a^x = b, 1.8.7 Reduce y = ax^n and y = ab^x to linear form, 1.8.8 The function y = e^x, 1.8.9 Gradient of e^kx (A-level only), 1.8.10 The function y = ln x, and 1.8.11 Exponential growth and decay. Each one has a worked solution and a mark scheme showing where the marks go.