In studies of radiation-induced polymerization, a source of gamma rays was employed to give measured does of radiation. However, the dosage varied with position in the apparatus, with these figures being recorded:
Position (in.) 0 0.5 1.0 1.5 2.0 3.0 3.5 4.0
Dosage (105 rads/hr) 1.90 2.39 2.71 2.98 3.20 3.20 2.98 2.74
The reading at 2.5in. was not reported, but the values of radiation there is needed. Fit a interpolating polynomial of various degrees (at 3 different polynomials) to the data to suppoly the missing information.
Compare each estimate with a cubic spline interpolation and estimate. What do you think is the best estimate for the dosage level at 2.5in.?

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position = [0 0.5 1.0 1.5 2.0 3.0 3.5 4.0];
dosage = [1.90 2.39 2.71 2.98 3.20 3.20 2.98 2.74];
D1 = polyfit(position,dosage,1); % polyfit for polynomial of degree 1
d1 = D1(1)*2.5+D1(2); % dosage at 2.5in for polynomial of degree 1
D2 = polyfit(position,dosage,2); % polyfit for polynomial of degree 2...

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