1. (Submit for Grading) Experiments with hospital patients tested their reaction in the morning to an auditory signal (a noise). The patient response time t (in milliseconds) is thought to be related to the patient's sleep time S (in hours) during the night. Table 1.1 below shows the experimental results. You have hypothesized that a power law model ts the sample data. Include the data as a table in the Problem statement. Table 1.1: Hospital patient sleep time and their response time to an auditory signal Sleep Response Time Time 5 : (llmus' (lilillisemuds a) Write the mathematical form of the hypothesized relationship between t and S. Show equations for both the original (untransformed) form and the linearized (transformed) form. Use symbols t and S for the variables, and m and b for the unknown parameters