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A person drinks a cup of coffee. Assume that the caffeine enters his bloodstream immediately and that there was no caffeine in his bloodstream before he drank the coffee. The half-life of caffeine in a person's bloodstream is about 6 hours. A cup of coffee contains about 240 milligrams of caffeine. a) Let f(t) be the number of milligrams of caffeine in the person's bloodstream at t hours after he drank the coffee. Find an equation for f. (Use 6 decimal places for rounded values.)

A person drinks a cup of coffee. Assume that the caffeine enters his bloodstream immediately and that there was no caffeine in his bloodstream before he drank the coffee. The half-life of caffeine in a person's bloodstream is about 6 hours. A cup of coffee contains about 240 milligrams of caffeine. a) Let f(t) be the number of milligrams of caffeine in the person's bloodstream at t hours after he drank the coffee. Find an equation for f. (Use 6 decimal places for rounded values.)

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter4: Exponential And Logarithmic Functions
Section4.CR: Chapter Review
Problem 13CC: Suppose that the initial mass of radioactive substance is m0 and the half-life of the substance is...
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4. A person drinks a cup of coffee. Assume that the caffeine enters his bloodstream immediately and that there was no caffeine in his bloodstream before he drank the coffee. The half-life of caffeine in a person's bloodstream is about 6 hours. A cup of coffee contains about 240 milligrams of caffeine. a) Let f(t) be the number of milligrams of caffeine in the person's bloodstream at t hours after he drank the coffee. Find an equation for f. (Use 6 decimal places for rounded values.) b) Assuming that the person drank the cup of coffee at 7 p.m. and that he has trouble falling asleep with more than 100 mg of caffeine in his system. How many hours will it take until enough caffeine is out of his system so that he can fall asleep (round using 2 decimal places)? c) Challenge: What time will it be?
Transcribed Image Text:4. A person drinks a cup of coffee. Assume that the caffeine enters his bloodstream immediately and that there was no caffeine in his bloodstream before he drank the coffee. The half-life of caffeine in a person's bloodstream is about 6 hours. A cup of coffee contains about 240 milligrams of caffeine. a) Let f(t) be the number of milligrams of caffeine in the person's bloodstream at t hours after he drank the coffee. Find an equation for f. (Use 6 decimal places for rounded values.) b) Assuming that the person drank the cup of coffee at 7 p.m. and that he has trouble falling asleep with more than 100 mg of caffeine in his system. How many hours will it take until enough caffeine is out of his system so that he can fall asleep (round using 2 decimal places)? c) Challenge: What time will it be?
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