Problems 1. The following equation describes the process of warming a hot tub by adding hot water: IN-ISTART) where is the temperature of the water in the hot tub is the temperature of the water flowing into the hot tub, (130F) is the initial temperature of the water in the hot tub (65F) is the hot-water flow rate (5 gpm) is the volume of the hot tub (500 gallons), and is the elapsed time since the hot water started flowing TIN TSTART Create an x-y plot that shows how thehot tub water temperature (T) increases over time (t). Your temperatures should be plotted from 65F up to 110F. You may have to extend your time vector until it causes the temperature to exceed 110F. Identify each major temperature data point (increments of 5F) on your plot. Add a textual annotation to your plot that lists the approximate time at which the tub's water temperature first reaches 110F. If the hot-water flow rate was increased to 10 gpm, how long would it take for the water temperature in the tub to reach 110? Again, you may have to extend your time vector until it causes the temperature to exceed 110F Have MATLAB draw a second plot, representing this second set of data on the same graph as the first plot. Add a second textual annotation for the second plot. Include a legend that identifies each plot. a. b