2. Suppose you have an 8 oz glass of wine. How many standard drinks is this?

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1 Math 212 Drinking and Driving Project Part I: Reading the Charts Every year, people are killed in accidents due to driving while intoxicated. This project will examine the effects of drinking on a person s ability to safely operate a motor vehicle. Throughout the project, assume that the alcohol specified is consumed on an empty stomach. For the following questions, refer to the tables attached to this project worksheet. 1. Suppose you have one 12 oz. can of beer. How many standard drinks is this? 2. Suppose you have an 8 oz glass of wine. How many standard drinks is this? 3. Suppose you have a rum and coke with 2 shots of rum in 8 oz of coke. How many standard drinks is this? Assume that Robert, a 160 pound male, has two 12 oz. beers. 4. What is Robert s blood alcohol level? 5. In California, it is illegal for an adult (over 21) to drive with a blood alcohol level of or higher. If he were to drive at this point, would he be driving illegally? 6. Consult the table showing the effects of alcohol consumption. What effects might this level of intoxication have on his driving? Robert s girlfriend, Margie, who weighs 120 pounds, also has two 12 oz. beers. 7. What is Margie s blood alcohol level? 8. If Margie were to drive, would she be driving illegally? 9. What effects might this level of intoxication have on her driving?

2 Part II: The Facts of the Case These are the basic facts from a jury trial during the summer of It was a DUI case. Read through the evidence presented. Your group is the jury. Would you find the defendant guilty of a DUI? The defendant was a 120 pound female. At approximately 8:30 pm she and a friend each had a mixed drink at a bar in Santana Row. Her friend had a Cosmopolitan (Vodka and Cranberry juice). The type of drink that the defendant had was not specified. Neither its size nor the number of shots of alcohol in the drink was specified. At approximately 10:15, the defendant hit another car while merging onto the 880 freeway. Both cars pulled over. The driver of the other car observed some slurred speech from the defendant. Insurance information was exchanged and the defendant then left the scene. The other driver waited for the police to arrive. She gave the defendant s insurance and license information to the officer. The insurance information was later found not to be that of the defendant. The correct address was found using the vehicle license information. At approximately 12:30 pm, the officer arrived at the defendant s home. She had been home for approximately 30 minutes. The officer observed a strong smell of alcohol. He asked the defendant if she had had anything to drink since arriving home. She stated that she had not. He performed a series of field sobriety tests on the defendant, which she failed. He then placed her under arrest. At approximately 1:30 am, she was given a blood alcohol test. The reading was, above the legal limit. During the trial, the defense stated that the defendant s statement to the officer that she had not had anything to drink when she arrived home was incorrect. She had drunk a half a glass of wine with her father at about 12 midnight. The amount of wine drunk at this time was stated, at various times in the trial, to be between 6 and 8 ounces. The defendant did not testify on her own behalf during the trial.

3 Part III: Analysis of the Evidence 1. Suppose the defendant had a Cosmopolitan at 8:30 like her friend. Assume the drink contained 2 shots of vodka. a. How many standard drinks would this be? What would the defendant s blood alcohol after she finished her drink? b. Let B be the defendant s blood alcohol level t hours after she drank the Cosmopolitan. On average, the body will metabolize the alcohol and the person s blood alcohol level will decrease kt exponentially by percent per hour. Write an exponential model in the form B = a e for her blood alcohol level. c. Use your model to complete the table below. t = time since drinking (hours) B = blood alcohol level d. Use your table to draw a graph of the defendant s blood alcohol level versus time. Make sure you label your axes and scale each axis evenly. Use a ruler to draw your model. e. What would the defendant s blood alcohol level have been at 1:30 am, when she was given the blood test? Is this consistent with the results of the test? Explain. f. What would the defendant s blood alcohol level have been at 10:15 when the accident occurred? Would this have been over the legal limit of?

4 2. Let s work backward from the blood test. We can use a model to determine what the defendant s blood alcohol level was in the past. This is called retrograde analysis. (Retrograde means backward) a. What was the defendant s blood alcohol level as measured at 1:30 am? b. Let B be the defendant s blood alcohol level t hours after her blood test. Write an exponential kt model in the form B = a e for her blood alcohol level, again using the fact that the blood alcohol level will decrease by percent per hour. c. Since we want to determine the defendant s blood alcohol level prior to the test, we will project backwards in time. Use your model to complete the table below. Explain why the values in the first column are negative. t = time since drinking (hours) B = blood alcohol level d. Use your table to draw a graph of the defendant s blood alcohol level versus time going backwards in time. Make sure you label your axes and scale each axis evenly. Use a ruler to draw your model. e. What would the defendant s blood alcohol level have been at 8:30 pm, when she drank her Cosmopolitan? How many standard drinks would she have had to drink to achieve this level of intoxication? f. What would the defendant s blood alcohol have been at 10:15 pm when the accident occurred? Look at the chart on the last page of this project. What effects would she have exhibited with this

5 level of intoxication? (You will have to judge, since it is between the levels indicated.) Is this consistent with the evidence provided? Explain. g. Based on the above calculations, do you think that the only alcohol consumed by the defendant was the one Cosmopolitan at 8:30? Give a reason for your answer. 3. The defense claimed that the defendant actually had an 8 ounce glass of wine at 12 midnight. a. How many standard drinks are equivalent to 8 oz. of wine? What would the defendant s blood alcohol level have been after finishing this glass of wine? (For now assume no other alcohol in her blood) b. Let B be the defendant s blood alcohol level t hours after she drank the glass of wine. Again, use the fact that the blood alcohol level will decrease by per hour. Write an exponential model kt in the form B = for her blood alcohol level. a e c. Use your model in 3b. to determine the defendant s blood alcohol level at 1:30 when she was given the blood alcohol test. Is this consistent with the results of the test? Explain. 4. In the last question, we assumed that there was no other alcohol in the defendant s system except for the glass of wine. However, in fact, there would be some residual alcohol in her blood from her drink at 8:30. Remember that no testimony was given regarding how much the defendant had drunk at that time. Let use analyze that situation. a. The defendant s blood alcohol level was percent at 1:30 am. From this, subtract your answer to 3. c. above, the blood alcohol level as a result of the wine she drank at 12 midnight. This will leave you with the amount of the blood alcohol level that was a result of the drink she had at 8:30. Show your calculations below. b. Using your answer to the last question as the initial amount, write an exponential equation for the defendant s blood alcohol level after t hours, again using the fact that the blood alcohol level will decrease by per hour. Write your answer below.

6 c. We will now use retrograde analysis to determine what her blood alcohol level would have been at the time of the accident by tracing only the alcohol from the original drink. How many hours before the blood test was her accident? Estimate the defendant s blood alcohol level at the time of the accident using your equation in 4.b. above. Remember, we are going backward in time, so time should be negative. Show your work below. d. According to your answer in part 4c, was the defendant s blood alcohol level at or above the legal limit of percent? From the chart on the last page, write down some of the effects on driving for this level. Are these effects consistent with what was reported in the trial evidence? Part IV: Your Verdict Please! Look over the evidence given in the trial and your answers to the questions asked in the Part III: Analysis of the Evidence portion of the project. Would you find the defendant guilty of a DUI? Write a paragraph of at least 5 sentences with your decision regarding her guilt or innocence. Use the results of questions 1 5 to justify your decision. The more math you use to defend your choice, the higher your score will be.

7 Male Female Drinks Table 1: Approximate blood alcohol percentage (by vol.) [3] One drink has 0.5 US fl oz (15 ml) alcohol by volume Body weight 40 kg 45 kg 55 kg 64 kg 73 kg 82 kg 91 kg 100 kg 109 kg 90 lb 100 lb 120 lb 140 lb 160 lb 180 lb 200 lb 220 lb 240 lb Table 2: Definition of 1 Standard Drink Alcohol Amount (fl oz) Serving size Alcohol (% by vol.) 80 proof liquor 1.25 oz. One shot 40 Table wine 4 oz. One glass 12 Beer 12 oz. One can 4.5 Source: Retrieved Oct 22, 2012

8 Table 3: Effects of Various Blood Alcohol Concentration Levels Source: Retrieved Oct 22, 2012