Caffeine Effects:

The Math Behind It

Background Information

Caffeine is found in many of the foods and products that we use daily. Things like chewing gum, peanut butter, and many lotions. Caffeine is a stimulant That may speed up reactions. Some other side effects include diarrhea, insomnia, and nervousness. Depending on your weight and size caffeine may leave your body at different rates. However, you no longer feel these effects after you have about 32 mg. of caffeine left in your body. The universal rate at which caffeine leaves your body is 13%.

The Math Behind It

If you thought about the consumption of caffeine as a function, it would be an exponential function. An exponential function is when a numbered id constantly multiplied over a fixed period of time. Considering the function, y=52(.87)^x 52 is the y-intercept and in terms of the project that means 52 is how much caffeine was consumed at the beginning of the 48 hours. Because this is an exponential function we know that it can never be 0 so, that means the caffeine will never completely leave our bodies. The time after the caffeine will no longer have an effect on your body is 3.5 hours. The time at which caffeine will be half way out of your body is 5 hours. This is all considering our starting amount of caffeine is 52 mg. So, if your starting amount is different your numbers may vary.

Based on my research I suggest that you stop drinking coffee up to hours before you go to sleep. I recommend this because it takes up to 4 hours for half of it to be gone and the rate at which the caffeine leaves will begin to slow down drastically. So, if you consume a large amount of caffeine before bed your mind will not be at rest. If you would like to enjoy a good night's sleep stop that consumption early!

My study results are shown below in this graph. Also, a link will be attached.

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