![]() ![]() ![]() For our simulation let's just assume an even 100 mg per cup of coffee. The caffeine content in a typical brewed coffee ranges between 80 to 135 mg in a 7 ounce cup of coffee. Let's start with a coffee drinker who ingests 6 hours of coffee per day. Now we want to set up a simulation of your daily caffeine habit. Usually they are more complicated so rather than spend a lot of time working out an exact solution it is often more prudent to just use a solver. I typically do not use formulas like this because in real life situations it is rare to find such a clean and simple relationship. There is an explicit formula that you can use to determine the half-life coefficient and it can be found here. ![]() This is one good reason why you don't want to drink coffee after the lunch hour.Īside: Why Not Just Use The Half-Life Formula? Looking at the graph you also notice that the coffee elimination is fast at first and then it becomes slower and slower. In a further 6 hours (t = 12 hours) the concentration drops to 0.25 as expected. We see that at 6 hours the concentration (y-axis) drops to 0.5. Here is a graph of the result of using this coefficient. This saves you a lot of tedious trial and error and is a very handy feature in Excel. The cell we want Excel to change is B1 so just select cell B1 and press OK.Įxcel will find the value of B1 that will make the value in B9 equal to 0.5. We want it to be equal to 0.5 so set the second field to be equal to 0.5. Set the target cell to B9 (first field in the dialogue below). Now let's go to the Excel solver (called goal seek) as shown below: To start just put any number in that cell between 0 and 1. By the definition of half-life we know that at time t = 6 hours it must be equal to one-half (i.e. Each hour we multiply the previous value by some fraction to be determined soon. Then in column A we set up a small series from time 0 to time 6 hours. I set it to 1 to make the math easier to understand. Here we just start with an arbitrary amount in cell B3. In the 6 hours following that they eliminate half of the remaining amount (12.5% left). In the following 6 hours they eliminate half of the remaining amount (25% left). In the image above we determine the half-life coefficient for a typical person who eliminates half of the caffeine in their body in 6 hours (50% left). Here we are going to simulate the caffeine concentration in your bloodstream as a function of time through the day. ![]() This no doubt explains why I was able to consume vast amounts of coffee while being little affected. Supposedly this decreases heart attack risk, although other studies show caffeine is generally good for the heart. Unlike the majority of people, caffeine is broken down faster in your liver, so it has less effect on you. I had my DNA analyzed by 23andMe and then re-assessed using the Promethease DNA genotype system and I learned that I was a fast caffeine metabolizer (i.e. The half-life for the typical person is somewhere between 4 to 6 hours. I believe that without caffeine there would be no mathematics.Ĭaffeine is a drug that you metabolize and eliminate and this means that you can describe its reduction fairly well via the half-life mathematical method. In fact, when I was in University I was quite the coffee fiend drinking at least 6-8 cups a day, even well into the evening. You don't want to get caught slacking off.Ĭaffeine is the world's most popular psychoactive drug and it is my drug of choice.You work at a computer and have access to Microsoft Excel.If you have read my posts before you already know that there are a few prerequisites for this: This is the 7 th in my series of killing time at work using math (the others are listed at the bottom of this post). ![]()
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