EXAMPLE 6.1-1 Temperature Dynamics The temperature of coffee cooling in a porcelain mug at room temperature (68°F) was measured at various times. The data follow. Timer (sec) 0 620 2266 3482 Temperature I (F) 145 28 130 103 90 Develop a model of the coffee's temperature as a function of time, and use the model to estimate how long it took the temperature to reach 120°F. Rate Temperature (deg) Relative Temperature (dagF) 30 188 40 50 1000 2000 Time() 3000 4000 Reative Temperature (deg) 1000 2000 3000 4000 Time (sec) 140 Sepurdue 130 120 110 100 90 80 1000 2000 3000 4000 1000 T 2000 3000 4000 Time() Figure 6.1-3 Temperature of a cooling cup of coffee, plotted on various coordinates.