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Quenching is the process of immersing a hot metal object in a bath for a specified time to obtain certain properties such as hardness. A copper sphere, 38.1mm in diameter, initially at 305°C. is immersed in a bath at 0'C. The following table gives measurements of the sphere's temperature versus time. x(x) 0 Temp (C)) 305 1.0 251 2.0 132.5 3.0 93 4,0 28.5 5.0 5.0 Assume an exponential model of the form: Tit) de a Linearize the model and find a and 3 coefficients using polyfit. 6.0 0.5 b. Calculate the coefficient of determination, correlation coefficient and the standard error of the estimate. c. Make a subplot with the non-transformed data and regression model in the top half. Subplot the linearized model with transformed data and regression line in the bottom half. Fully annotate the plot. For the plot, in the top half, use a black color line, linewidth-2, marker: circle, color red. In the bottom half, use a blue color line, linewidth-2, marker: diamond, color green. a. Estimate the time necessary to quench the sphere to 34.5°C.