A person drinks a cup of coffee. We assume tht the caffeine enters his bloodstream immediately, and that there was no caffeine in his bloodstream prior to drinking the coffee. The half-life of caffeine in a person's bloodstream is about 6 hours. A cup of coffee contains about 100 milligrams of caffeine.
a. Let f(t) represent the number of milligrams of caffeine in the person's bloodstream at t hours after drinking the cup of coffee. Find an equation of f
b. The person drinks the cup of coffee at 8 am and goes to bed at 11 pm Use f to predict the amount of caffeine in his bloodstream when he goes to bed.
c. Suppose the person drinks another cup of coffee 24 hours after the first cup. How much caffeine will be in his bloodstream from these 2 cups of coffee just after drinking the second cup? Explain how you can find this result without using an equation?
d. Now assume that the person drinks the cup of coffee at 8am and then drinks a cup of coffee every morning at 8am from then on. Sketch a qualitative graph that describes the relationship between caffeine in the person's bloodstream and time. Describe any assumptions that you make.