### Caffeine and it's Effects on the Body

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.

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

32-200 mg

Is caffeine a stimulant or a depressant?

Caffeine is a stimulant.

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:

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

Sunkist Orange Soda: 12 fl oz.

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.

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.

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.

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.