(20 points) Using your equation from 3a) a. When is the amount of caffeine increasing and decreasing for (assuming no additional caffeine is consumed) b. What is the rate of change of caffeine in the body after 5 hours? ____________mg/hr c. What is the rate of change of caffeine at the time when the person stops feeling the affects of the caffeine (answer from 3c)? d. What appears to be happening to the amount of caffeine over time? Do your answers from the above three parts support your answer? Explain why or why not.

(10 points) Go online and find the amount of caffeine in your favorite caffeinated beverage. Whether it is a Starbucks coffee or latte, a soda, or an energy drink.

a. List that amount here. ___________________

b. Using your k value from 3a) and your caffeine amount listed above in 5a), write an exponential function representing the breakdown of the caffeine in your body using our format of .

6. (25 points) Assume you have that drink at the start of our class (1:00 pm).

a. Using your equation at what time will you have half of the original amount in your system? Based on your drink, how much caffeine will be in your system at that time?

b. What time do you usually go to sleep? Will you still feel the effect of the caffeine when you go to sleep? (i.e. will the caffeine be reduced to the minimum amount that it should no longer have any stimulant effect on your body?) Explain why or why not.

c. Given that you might drink multiple caffeinated beverages each day and that certain foods also contain caffeine, does this information change the way you think about having caffeinated food and beverages? Explain why or why not