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Question: 4 (25 Points): A pavement design is summarized in Table 1. The fitted sigmoidal function coefficients and the shift factor second polynomial function coefficients for the dynamic modulus master curve of the asphalt concrete are given in Table 2. Note that the values of those parameters are based on a dynamic modulus unit of psi and a Fahrenheit temperature unit. The frequency temperature superposition for shifting of the dynamic values was performed at a reference temperature of 70 °F. Table 1. Pavement design. Layer Thickness (in.) Modulus Asphalt Concrete 6 See Table 2 Aggregate Base 10 34,000 psi Natural Subgrade soil Infinite 13,000 psi Table 2. Dynamic Modulus Master Curve Parameters Parameter Value 8 3.7658 a. 2.8811 B 1.3604 Y 0.4282 0.000142 b -0.09330 5.8352 a C Other information you will need and/or assumptions you may make include: • Traffic speed = 60 mph (equivalent to 10 Hz at the middle of the AC layer). • Temperature will not vary within the pavement layer The asphalt concrete layer does not age • Average pavement temperature in October = 100 °F • Standard deviation of pavement temperature in October = 10 °F a) Determine the five quintile temperatures in October. (10 points) b) Determine the dynamic modulus values of the AC layer at the five quintile temperatures in October at the middle of the AC layer. (15 points)