Analysis of Caffeine Consumption
Have you ever wondered exactly at what rate caffeine will leave the body, and to what extent will we feel it’s effects? How long it takes for there to be nearly no caffeine left in the body? How long it would take for the amount of caffeine to make no difference to the body? Caffeine is primarily used as a stimulant for consumption in commercial drinks and very few food items. You can find caffeine in many things you consume every day, like tea, soda, coffee, energy drinks, and even chocolate. We have observed that caffeine is eliminated by the body at a rate of 13%/hour. For example; if you have 100mg of caffeine in your body, after 1 hour there will be 87mg of caffeine left in the body. This is an example of exponential decay; this is where decay can be observed by a percentage rather than an amount. This is important because this makes the decay in the beginning in the hour as an amount larger than the amount of decay in the end as milligrams in this case. This also forms an asymptote. This is where the amount can mathematically never reach 0, this is because there is always room to remove a percentage of a total amount, even if the starting amount or the answer are not even measurable by an computer. Even there is no way to get rid of the caffeine, our body can’t feel the affects of this after caffeine count becomes less than 32 mg. So on average it is best to stop drinking caffeine 4-5 hours before you go to bed. This depends greatly on the drink you have and how much caffeine it has, but 4 to 5 hours is a safe time before you go to bed so that the caffeine in your body will be at most considered a minor stimulant.
This kind of graph is called a piece-wise graph. This is where the function changes, making the graph “jump” from, in this case, one y-value to another. This piece-wise only shifts on the y-axis because x is representative of time, which can’t be skipped or altered. “x=32” represents where caffeine would no longer affect the body at all. “16≤x≤27” shows where I slept, from 10 o’clock pm to 9 o’clock am (I was tired okay?). The functions themselves are in a specific format; y=a(b)x. In an example of the equations that I had it would be; y=90(.87)(x-1). In this case, “90” represents the amount of caffeine I started off with after drinking the first drink. “(.87)” is the multiplier, it’s the difference of the removal of the the 13% from each hour. “(x-1)” represents the exponent that is the number of hours minus the difference from the starting hour (6 o’clock am on the first day).