The stopping distance of an automobile, on dry, level pavement, traveling at a speed v (in kilometers per hour) is the distance R (in meters) the car travels during the reaction time of the driver plus the distance B (in meters) the car travels after the brakes are applied (see figure). The table shows the results of the experiment. Speed, v 20 40 60 80 100 Reaction Time Distance, R 8.2 16.6 24.9 33.2 41.6 Braking Time Distance, B 2.2 8.9 20.1 35.7 55.8 (a) Use the regression capabilities of a graphing utility to find a linear model for the reaction time distance R. (Round numerical values to four decimal places.) R(v) = (b) Use the regression capabilities of a graphing utility to find a quadratic model for braking distance B. (Round numerical values to four decimal places.) B(v) = (c) Determine the polynomial giving the total stopping distance T. (Round numerical values to four decimal places.) T(v) = (d) Use a graphing utility to graph the functions R, B, and T in the same viewing window. (e) Find the derivative of T. (Round numerical values to four decimal places.) T '(v) = Find the rates of change of the total stopping distance for v = 40, v = 80, and v = 100. (Round your answers to four decimal places.) T '(40) = T '(80) = T '(100) =