2 HiMAP Pull-Out Section: Spring/Summer 2005 IN AN 8-OZ CUP OF COFFEE A round the world, people enjoy caffeine in both food and drink. Caffeine is an alkaloid compound that comes from plants, including APPROXIMATE AVERAGE AMOUNT OF CAFFEINE coffee, tea, kola nuts, mate, cacao, and guarano. Some people drink caffeine drinks because they like the taste, and some drink them for the physical effect they can have. Most people are aware of differences in the Drip 165 mg way they feel as a result of drinking caffeine; it stimulates the central nervous Brewed 130 mg system, the heart, and the respiratory system. For many people, the effect is Instant 95 mg pleasant and energizing, a "wake up" or a "pick-me-up, " and a way to delay Decaffeinated 4 mg fatigue. But for others, the effects are unpleasant. Laboratory tests indicate that one to three cups of coffee can increase a person's capacity for sustained intellectual effort and decrease reaction time (that's good) but may adversely affect the ability to perform tasks involving delicate muscular coordination and accurate timing (that's bad). APPROXIMATE AVERAGE AMOUNT OF CAFFEINE IN AN 8-OZ CUP OF TEA In this article, we explore the dynamics of caffeine in the body through the use Brewed of exponential functions. 45 mg Instant 35 mg Green tea 30 mg The amount of caffeine in food or drink can vary. Manufactured products such as sodas and candy bars have consistent levels of caffeine, but coffee and tea and other drinks have varying amounts. The "approximate average" amounts given in the tables at the left give us a reasonable picture, however. AMOUNT OF CAFFEINE The effects of caffeine can only be felt when sufficient amounts are present. For IN A 12-OZ SODA: most people, 32 to 200 mg of caffeine acts as a minor stimulant; these amounts have been shown to speed up reactions in simple routinized tasks in a Coca Cola 45.6 mg laboratory setting. As noted above, such minor stimulant effects are Diet Coke 45.6 mg experienced by some people as pleasant, but for others they are unpleasant. Surge 51 mg Steadiness of the hand has been shown to deteriorate when there is more than Dr. Pepper 39.6 mg 200 mg of caffeine present. More than 300 mg is enough to produce temporary Pepsi 37.2 mg insomnia. 480 mg has been shown to cause panic attacks in panic disorder Diet Pepsi 35.4 mg patients. Amounts of 5 to 10 grams (5,000-10,000 mg) of caffeine cause death. Mountain Dew 55 mg Chemicals are eliminated from the body in two primary ways: (1) through filtration by the kidneys, and (2) metabolism by enzymes from the liver. The kidneys tend to filter out a constant proportion of the chemical, that proportion depending on what the chemical is and the individual. In the "average person," AMOUNT OF CAFFEINE IN A about 13% of the caffeine present at the beginning of each hour is eliminated 1.5-OZ CHOCOLATE BAR during the hour. So: Hershey's Special, dark chocolate 31 mg Hershey Bar, You Try It #1 milk chocolate 10 mg If a person starts the day by drinking 3 cups of coffee (one right after the other) containing 130 mg of caffeine each, assuming the caffeine is absorbed into the body immediately, Amount of caffeine a. How much caffeine will there be in this person's body 1 hour later? 2 present in body Effect hours later? 3 hours later? 32-200 mg Minor stimulant b. Reflect on how you computed the answers to part (a) to help you develop More than 200 mg Unsteady hands a simple expression that gives the amount of caffeine in this person's body More than 300 mg Temporary 24 hours later, assuming no additional caffeine is consumed. Find the Insomnia amount. You do not need to compute the amount of caffeine in the body one hour Panic attacks in after another until you reach 24; you can find this amount directly. 480 mg panic disorder patients Let's explore this further. 5000 mg May cause deathIn this Investigation you will explore an application of exponential functions. The goal of this assignment is to apply the skills you learned in the last unit and see how exponential functions are applicable to your lives. Please see the attached file for the project information and questions. WakeUpandSmellTheCoffee.pdf Here is what I need you to submit. Type a report that includes the following: 1. An introduction that gives an overview of this Investigation. 2. Answers to all the questions for You Try It 1 - 7. Include any tables that you were asked to make. Include all required graphs in the document. Make graphs using Desmos (www.desmos.com). 3. Discussion: Post your You Try It #4 table and graph in the Investigation 2 Discussion forum. Reply to two other students. In your replies you can: Ask students clarification questions Share methods and strategies for making the graph and help each other with the process Compare your caffeine consumption with that of your group members 4. Write a conclusion paragraph reflecting on the work you did, the math you used and your opinion of the investigation and the results that you got. Submit one file in pdf format by clicking Submit and uploading your file. Here is a sample of a table used to track caffeine consumption over a 24 hour period and the functions and graph that models the caffeine consumption: Caffeine Consumption.pdfCaffeine Consumption Time of Caffeine Intake 6:30 am 9:00 am 3:00 pm 5:00pm 7:00pm 9:30pm Amount of caffeine in body before consuming 31.77mg 33.29mg 59.71mg 68.66me 80.24mg the caffeine Amount of caffeine in this drink or food 45mg 45me 45.6mg 31mg 45mg 45me Function that describes amount of caffeine in your body from now f(t) =45(.87) fit) =76.77(.87)t-2.5 f(t) =78.89(.87)tas f(t) =90.71(.87)t-105 f(t) =113.66(.87)1-12.5 f(t) =125.24(.87)t-15 until your next caffeine Oct 15 consumption + 45(.87)" (0