### Algebra 2: Caffeine Benchmark

Introduction

Do you drink coffee every morning? Do you like drinking soda? Did you ever wonder how much caffeine you consume in a 48-hour period? Have you ever wondered how caffeine can affect your body? Do you ever wonder what happens to the caffeine after it’s been in your body for a few hours? If you’ve answered yes to any of these questions then continue reading to find out how caffeine affects your body!

Caffeine is a drug that stimulates the central nervous system, to make us more alert. Caffeine can be found in drinks, such as coffee, ice tea, and soda. It is also found in chocolate, and some gum! Everyday people take in amounts of caffeine (mg). Your body starts feeling effects of the caffeine between 32-200 mg. Your body starts to eliminate 13% of the caffeine you intake each hour!

For example, I recorded six entries of the amount of caffeine that I consumed in a 48-period starting at 6:00 am. I gathered all my information and got the following results in the table below

Caffeine doesn’t leave your body immediately, it takes hours to get rid of caffeine in your body, but in the table above you can see that I consumed more caffeine each time I drank something, you may ask how much caffeine is in your body each time you drink a new caffeinated drink? To figure this out we use exponential functions! Exponential functions are functions that have a constant rate of change, we use the following equation to solve these functions: y=abx . A is the initial change, b is the ratio of change. Caffeine is an example of exponential decay because it’s decreasing as a constant rate.

The following table shows how much caffeine was in my body each time I drank a new caffeinated drink:

As you can see I used the exponential equation each time I consumed caffeine. For each new equation the ratio of change is 0.87 because that’s how much caffeine is left in your body in each hour (13% of caffeine leaves your body every hour). The exponent in the equation I subtracted the number of hours since the start of the day by T (x). I used the curly brackets to show how much caffeine decreased each time I drank something, to show when it stopped.