Task 1:

Make a conjecture: How long would you judge it takes for the caffeine to leave your body and at what rate?  At what point in time has half the caffeine left your body?

I would judge that it takes 6-8 hours for Caffeine and leaves your body at an hourly rate. So, at about 3-4 hours, the caffeine would be halfway gone.

Sketch a graph with labeled axes that shows what you think displays the relationship between time and the amount of caffeine in your body.  

1. What is the lowest amount of caffeine that can be present in the body to feel its effects?

32-200 mg

2. Is caffeine a stimulant or a depressant?

Caffeine is a stimulant.

3. What percentage of caffeine in a person’s body is eliminated each hour?

13 percent of caffeine is eliminated from the body every hour.

Task 2:

1. Choose a caffeinated drink you drink daily (or often).  

Sunkist Orange Soda: 12 fl oz.  

2. What type of function can you use to represent the amount of caffeine in your body?  Explain

You can use an exponential function to represent the amount of coffee in your body. You use this function because its graph decreases which is what happens to the caffeine as time progresses and it doesn’t decrease at a constant rate.

3. When will the caffeine completely leave your body?

Theoretically, the caffeine will never leave your body. This affects the math because on the graph, your asymptote will be 0 meaning the caffeine will never be completely gone.

4. When you have half of the caffeine left?  How long does it take for the first half to disappear?  How long for the second half?  Show this algebraically.

In order to find out when you will have half the caffeine, you would take your initial amount of caffeine (47 in my case) and divide it by 2. This is shown on the graph represented by the horizontal purple line.

5. When will the initial caffeine be reduced to an amount that should no longer have any stimulant effect on the body?  (Refer to the reading to determine what this amount typically is.) Mark this point on your graph.

The initial caffeine will be reduced to an amount that should no longer have any stimulant effect on the body after the average amount of 32 mg.

My Graph: The Relationship between time and the amount of caffeine throughout a 24 hour period.

Based on my research I recommend that caffeine should not be consumed regularly. The amount of caffeine you consume can increase quickly if you constantly consume it. Based on the amount of caffeine in the product, I would only recommend taking in one or 2 sources of caffeine each day and to space each intake out.

Have you ever wondered the effects of caffeine? Have you experiences the effects of caffeine? What is caffeine, a stimulant or depressant? Why does it stop affecting our system after a few hours? How much leaves and stays in the body each hour?

Caffeine affects our Central Nervous System (CNS), muscles, hearts and blood. Caffeine is most commonly used as a stimuli, to raise mental awareness. But, it is also used in herbal, pain-killer medicines, low blood-pressure and weight loss. Thus, caffeine is a stimuli, not a depressant. Caffeine affects restlessness, nervousness, irregular sleeping patterns (excessive) and stomach irritation.

Caffeine also makes its’ exit out of the body even hour. Research from the National Science Foundation reports, in an average person, 13% of the caffeine consumed is decreased every hour. This means, 87% still remains in the body. Every drink that consists of caffeine, hourly it will decrease by 13%.

To put this into work, I tracked the amount of my caffeine consumption over a course of 48 hours. The time began from 6:00 AM on Sunday, May 29 to 6:00 AM on Tuesday, May 31. Within these two days, drink items that included caffeine were; black tea, masala chai, Pepsi-Cola and iced coffee.

ANALYSIS OF EQUATIONS

Over the course of 48 hours, I consumed caffeine seven times. Each time caffeine was consumed, a different equation was created:

• The first equation (in red) was y=67(0.87)^x-0.5 of masala chai, drank after 30 minutes of 6 o’clock in the morning. It consisted of 67 milligrams of caffeine. However, the 67 in the equation derives from the amount of caffeine at 6:30 AM, saying we drank and finished the masala chai at 6:30 AM.

• The second equation (in purple) was y=235.38(0.87)^x-4.5 of Dunkin Donuts small iced coffee. It was consumed at 10:30 in the morning, 4.5 hours after 6:00 AM. The coffee itself instilled 197 milligrams of caffeine. But, even after 4.5 hours the previous caffeine consumption was still in my body, 38.38 milligrams. So, 197 and 38.38 were added to get the total caffeine present in my body at 10:30 AM.

• The third equation (in black) was y=149.07(0.87)^x-10.5 of black tea with 47 milligrams of caffeine. It was consumed 10.5 hours later from 6 in the morning. The number 149.07 comes from the previous amount of caffeine present in body at that time, 102.07 mg, then an addition of 47.07 milligrams.

• The fourth equation (in blue) was y=131.64(0.87)^x-16.5 of Pepsi consumed. It was consumed after 16.5 hours counting from the 6:00 in the morning. The number 131.64 comes from the amount of caffeine in the Pepsi 38.9 mg and the previous amounts at that time (just before consumption of Pepsi).

• The fifth equation (in red) was y=103.03(0.87)^x-25.75 of masala chai consumed on day two. The green shade represents from what to what time I was sleeping. Even during sleep the caffeine was releasing out of the body. So, 103.03 comes from the 67 mg in the masala chai, in addition to the previous amounts of caffeine within the body.

• The last, sixth equation (in red) y=91.72(0.87)^x-35 also represents masala chai being consumed after 35 hours (from 6:00 AM, previous day). As in the previous equations, 91.72 mg is of two “ingredients.” The already caffeine in the body, plus the additional caffeine being consumed from the drink, in this case 67 mg were added to the previous amounts of caffeine, 24.72 mg.

To break down the graph we have key features. They are features that best describe the graph, for an easier understanding. In terms of the graph, the red line represents 32 mg of coffee, the amount in the body that it is no longer in effect. The horizontal axis, x-axis represents the time in hours, while the vertical line, y-axis represents the amount present in my body.