As the food is digested the alcohol passes into the

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As the food is digested, the alcohol passes into the bloodstream through the walls of the small intestine. If the stomach is empty, however, the pyloric valve remains open. In this case, more than 80% of the alcohol goes straight into the small intestine, and as much as 20% passes into the bloodstream through the stomach lining, because there is no food to impede it. For this reason, alcohol absorp- tion on an empty stomach is much more rapid than on a full stomach. Once in the bloodstream, alcohol travels quickly throughout the body, permeating most body tis- sues in a matter of minutes or even seconds. About 90% of the absorbed alcohol is metabolized in the liver, where it eventually breaks down into carbon dioxide and water. About half the remaining 10% is excreted in fluids, such as sweat and urine, and the rest diffuses into the lung, from which it is exhaled. Table 1 The Case of Penicillin L1 L2 0 600,000 0.5 300,000 1.0 150,000 1.5 75,000 2.0 37,500 2.5 18,750 3.0 9,375 3.5 4,688 4.0 602,344
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-' 77D8K?<[email protected]:J7K<8:?<I7 s 7Mfc%7('+#7Ef%7(7¡78l^ljk7)'(' In this investigation and the accompanying activity sheets, students will compare the elimina- tion rates of caffeine and alcohol from the human body. In comparing these processes, they will learn about zero- and first-order drugs, exponential decay, half-life, and linear decay. FLI7I<=C<:[email protected] Teachers who include the topic of driving under the influence of alcohol as part of a first-year alge- bra course will not only teach applied mathemat- ics. They will also help students understand that, although alcohol is a legal substance for adults, all persons, regardless of age, need to learn how to protect themselves and others from the often-tragic consequences when people drive while intoxicated. The topic of DUI is of high interest to our stu- dents because they are just beginning to drive. As a result of this investigation, they seem to become much more aware of their own behavior and also more careful about whom they drive with. It is crucial that students find their own data, especially in investigations that deal with geographical and demographic differences. Students are always curi- ous and motivated by their findings—and that is a good thing. [email protected] :X]]\`e\7<c`d`eXk`fe7IXk\7?J_\\k7( 1. The scatter plot should look similar to the one shown in figure 1 . 2. Answers will vary but should describe the expo- nential decay of caffeine. 3. The equation of the best-fit curve to this graph is y = 48 0.794 x . 4. In this equation, a is the starting caffeine amount (in mg), and b is the fractional reduction of the caffeine amount per unit of time (mg/hr). 5. In any system that exhibits exponential decay, the term half-life describes the time it takes for the material present to diminish by half. Accord- ing to the data in question 1, the half-life of caf- feine in the body is 3 hours. (Actually, the half- life of caffeine varies widely in humans because age, pregnancy, smoking, and other factors influ- ence it. As with alcohol, caffeine is more rapidly absorbed on an empty stomach than a full one and for the same reasons. For the average adult, the half-life of caffeine is 3–6 hours.)
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