The cone and plate viscometer shown is an instrument used frequently to characterize non-Newtonian fluids. It consists of a flat plate and a rotating cone with a very obtuse angle (typically \(\theta\) is less than 0.5 degrees). The apex of the cone just touches the plate surface and the liquid to be tested fills the narrow gap formed by the cone and plate. The viscometer is used to measure the apparent viscosity of a fluid. The data below are obtained. What kind of non-Newtonian fluid is this? Find the values of \(k\) and \(n\) used in defining the apparent viscosity of a fluid. (Assume \(\theta\) is 0.5 degrees.) Predict the viscosity at 90 and \(100 \mathrm{rpm}\).

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Speed (rpm) 10 20 30 40 50 60 70 80 (N s/m) 0.121 0.139 0.153 0.159 0.172 0.172 0.183 0.185