Caffeine oecurs naturally in a variety of food products such as coffee, tea, and
ID: 3115967 • Letter: C
Question
Caffeine oecurs naturally in a variety of food products such as coffee, tea, and chocolate. The kidneys filter the blood and remove caffeine and other drugs through urine. The biological half -life of caffeine is approximately 6 hours. If one cup of coffee has 100 mg of caffeine, Che Guid Show Ask M Link to -t/6 then the amount of caffeine C (in mg) remaining after t hours is given by C 100(2)o. a. How long will it take for the amount of caffeine to drop below 70 mg? Round to 1 decimal place. b. Laura has trouble sleeping if she has more than 20 mg of caffeine in her blood stream. How many hours before going to bed should she stop drinking coffee? Round to 1 decimal place, if necessary.Explanation / Answer
a) plugging C = 70
70 = 100 (2)^-t/6
70/100 = 2^-t/6
0.7 = 2^-t/6
taking natural log on both sides
ln 0.7 = -t/6 ln 2
t = 3.0874
so, it takes approximately 3.1 hours to drop below 70 mg
b) plugging C = 20
20 = 100(2)^-t/6
20/100 = 2^-t/6
t = 13.9 hours
so, laura must stop drinking coffee 13.9 hours before going to bed