Caffeine is an alkaloid compound that comes from plants, including APPROXIMATE AVERAGE AMOUNT OF CAFFEINE A round the world, people enjoy caffeine in both food and drink. coffee, tea, kola nuts, mate, cacao, and guarano. Some people drink IN AN 8-OZ CUP OF COFFEE 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 of exponential functions. Brewed 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 You Try It #1 Hershey Bar, 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 after another until you reach 24; you can find this amount directly. Panic attacks in 480 mg panic disorder patients Let's explore this further. 5000 mg May cause deathYou Try It #2 If a person starts the day by drinking 3 cups of coffee containing 130 mg of HALF-LIFE caffeine each, assuming the caffeine is immediately absorbed into the body, The time it takes for the amount of a a. Write an equation in the form y = f(t) for the amount of caffeine in the substance present to be reduced by half is body t hours after ingesting 390 mg. called the half-life of the substance. b. Graph the function you developed in part (a). c. What is the long term behavior ("end behavior") of the function you graphed? What does that say about the 390 mg of caffeine the person drank in the morning? d. How much caffeine will be in the person's body 30 minutes after drinking 3 cups of coffee (when t = ?)? e. How long will it take for the 390 mg of caffeine in the person's body to be reduced to 195 mg? Read the definition of half-life in the margin carefully. The concept of half-life is applied to elimination of drugs from the body, and to radioactive decay, and to other situations. Note that half-life is a measure of time. It takes about 5 hours for 390 mg of caffeine to be reduced by half to 195 mg. Thus the half-life of caffeine in the body is about 5 hours. You Try It #3 To understand half-life, first determine how much of the original 390 mg of caffeine is in the body after two half-lives; then after three half-lives. Then determine the value of t, time, for each of these answers. Answer the questions You can get more Information on caffeine in the order they are asked; it will help you get a deeper understanding of the content from the Internet. Try, for example. half-life concept. http://coffeefaq.com/caffaq.html or http://www.coffeescience.org. Now we get personal. Time of caffeine 8:00 am 9:30 am You Try It #4 intake Amount of a. Make a table like the one at left to keep a record of your own caffeine con- caffeine in sumption over a 24-hour period beginning when you wake in the morn- body before 105.5 mg consuming ing. If you do not eat or drink caffeine, use data from a friend. Estimate this caffeine the amount of caffeine in the drinks or chocolate you consume using the information in the margin of page 1 or from product labeling. Assume that Amount of caffeine in 130 mg 40 mg the caffeine is consumed and absorbed by your body immediately, even this drink though you may actually linger over your drink and even though it will or food actually take a short time for your body to absorb the caffeine. Amount of caffeine in 130 mg 145.5 mg .. . b. From your table, sketch a graph of the amount of caffeine in your body (or body after your friend's) over this 24-hour period. this intake Function that c. Use your graph to help you write a conditional function (a piecewise- describes defined function) that shows the amount of caffeine in your body at any amount of time, t, during the day. To write a function using a single variable for time, caffeine in For 0 sts 1.5, For 1.5