31 Aug Math Word Problem
Why Can’t I Sleep?
The half-life of caffeine is about 5.7 hours. This means that half of the caffeine intake will still be in your system after 5.7 hours. The general formula (using rational exponents) is:
where:
t = the hours since drinking the caffeine
k = the half-life of caffeine (about 5.7 hours*)
C = the milligrams of caffeine ingested
A = the milligrams of caffeine left in your body after t hours
* Statland BE, Demas TJ. Serum caffeine half-lives. Healthy subjects vs. patients having alcoholic hepatic disease. Am J Clin Pathol. 1980 Mar;73(3):390-3. doi: 10.1093/ajcp/73.3.390. PMID: 7361718.
Find the amount of caffeine in your favorite caffeinated beverage by checking the nutrition label or doing research on the internet. Be sure to find the amount of caffeine in the entire container, not just in one serving. This will be C in the equation. Assume you drink the entire beverage in one sitting. Include the name of your favorite caffeinated beverage and the amount of caffeine in that beverage.
1) Calculate the amount of caffeine (mg) remaining in your body after t = 2 hours after you drank the beverage. Show all steps in your calculations and round your answer to the thousandths place (three decimal places.)
Now, consider different times of the day that you might drink caffeine and:
2) Pick a time between 11am and 6pm. Determine how many hours until 9pm (an approximate bedtime). This is your value for t. How much caffeine (mg) remains in your body at 9pm? Show all steps in your calculations and round your answer to the thousandths place (three decimal places.)
3) Reflect on your calculations. What effect might caffeine have on your work, exercise or other daily activities? When do you think you should drink your caffeinated beverage in order to get a quality night’s sleep?
