The progress of a drug through human body is a chemical kinetics problem involving first-order consecutive reactions. Gastrointestinal tract Eliminated drug Bloodstream Setting the scene. You are a physician in a hospital emergency room. A child has just been brought to the emergency room by a frantic parent. The parent takes the asthma medication, theophylline, in tablet form. Two hours before arriving at the hospital, the child ingested eleven 100 mg theophylline tablets. Like most oral drugs, theophylline is absorbed into the bloodstream at a rate proportional to the amount present in the gastrointestinal tract (stomach and intestines) and is eliminated from the bloodstream at a rate proportional to the amount present in the bloodstream. Your quick check of the Physician's Desk Reference (PDR) reveals that the brand of theophylline the child took has an absorption half-life of 5 hours and an elimination half-life of 6 hours. The PDR also wams that a blood-level concentration of 100 mg/L or more of the drug is seriously toxic and that a concentration of 200 mg/L or more is fatal. You estimate that the child has 2 L of blood. You also determine that, because of the 2 hour delay, the pills already have passed from the child's stomach to his intestines, so that it is too late to eliminate the drug from the child's body by inducing vomiting. Your task is to determine if the child is in danger, and, if so, to save his life. (1) G(T) is the amount of theophylline in the child's gastrointestinal tract (in mg) after 1 hours and B() is the amount of theophylline in the child's bloodstream (in mg) after 1 hours. Determine G(t) and B(t). Graph G(t) and B(t). (2) Determine the amount of theophylline in the child's bloodstream at time = 2 hours, the time of his admission to the hospital. Does the amount of theophylline in his bloodstream pose any danger to him at this time