The intensities of light I in a transparent solid were measured at different lengths of penetration L of the light. The data are: I =3.9, 3.7, 3.5, 3.3, 2.6, 2.2W/m 2 and L =0.19, 0.8, 1.3, 1.8, 4.1, 5.6cm respectively; the intensity of the incident beam I0 was equal to 4.7W/m 2 .Write the user-defined function named Problem_5_16 that fits the data by the nonpolynomial equation ? = a0.I0.exp(-a 1 L) where a 1 is the absorption coefficient. The function has no input parameters and has the output parameters coefficients a 0 and a 1 and R-squared. The results should be represented in the graph

The intensities of light I in a transparent solid were measured at different lengths of penetration L of the light. The data are: I =3.9, 3.7, 3.5, 3.3, 2.6, 2.2W/m 2 and L =0.19, 0.8, 1.3, 1.8, 4.1, 5.6cm respectively; the intensity of the incident beam I0 was equal to 4.7W/m 2 .Write the user-defined function named Problem_5_16 that fits the data by the nonpolynomial equation ? = a0.I0.exp(-a 1 L) where a 1 is the absorption coefficient. The function has no input parameters and has the output parameters coefficients a 0 and a 1 and R-squared. The results should be represented in the graph and in the table as follows: – the graph shows the original points, the fitting curve, and the best-located legend; – the table represents the original data, the fitting light intensities, and the residuals. Use the 1st degree polynomial fit by the polyfit command with L and log(I) as its the x and y parameters respectively; to calculate fitting values of the viscosity use the nonpolynomial function with a 0 =exp(a(2))/I 0 and a 1 =a(1) where a is the output coefficient vector of the polyfit command.

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