The following table gives the heat index (Heat Stress Index) as a function of the air temperature (Environ- mental Temperature) and the Relative Humidity. The heat index is measured in F, the air temperature is measured in F, and the relative humidity is measured in % . For this problem we will use the variables I (heat index), T (air temperature), and H (relative humidity). The table presents I(T, H). Table 3 Apparent temperature, Heat Stress Index (HSI) Environmental Temperature "F Relative Humidity 70 75 80 85 90 95 100 105 110 115 0% 64 69 73 78 83 87 91 95 99 103 10% 20% 65 70 72 75 80 85 90 95 100 105 105 111 120 66 67 77 82 87 93 99 112 30% 73 78 84 90 96 104 113 123 135 40% 50% 68 69 74 75 79 86 88 93 101 110 120 123 137 151 81 96 107 135 150 60% 70% 70 70 76 77 82 85 90 100 114 132 124 144 149 93 106 71 71 72 Apparent temperature ("F) Dangers 80% 78 86 97 113 136 Extreme Danger 90% 79 88 102 122 100% 80 91 108 Category Extreme danger Danger Extreme caution 90-105 Heat stroke imminent Heat exhaustion likely Heat cramps, exhaustion possible Exercise more fatiguing than normal Greater than 120 105-120 Caution 80-90 a. Estimate a value for Ir(90, 40) and interpret your answer. b. Estimate a value for I(90, 40) and interpret your answer. c. Give a general description of the contour curve given by I(T, H) = 100, that is explain how the idea of this contour curve makes sense in this problem. Note: Ir =