SOLUTION: The half-life of caffeine is approximately 5.7 hours and a shot of 5-hour Energy contains 200 mg of caffeine. How long after drinking a shot of 5-hour Energy will it take for the a

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Question 1005366: The half-life of caffeine is approximately 5.7 hours and a shot of 5-hour Energy contains 200 mg of caffeine. How long after drinking a shot of 5-hour Energy will it take for the amount of caffeine in a person's system to decay to 80mg? Label your answer and round it to one decimal place. Recall: A=A02^-t/h
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The half-life of caffeine is approximately 5.7 hours and a shot of 5-hour Energy contains 200 mg of caffeine.
How long after drinking a shot of 5-hour Energy will it take for the amount of caffeine in a person's system to decay to 80mg?
Label your answer and round it to one decimal place.
:
Ao*2^(-t/h) = A, where
Ao = 200
A = 80
h = 5.7 hrs
t = time of decay
:
200*2^(-t/5.7) = 80
2^(-t/5.7) = 80%2F200
2^(-t/5.7) = .4
using nat logs
-t%2F5.7ln(2) = ln(.4)
-t%2F5.7= ln%28.4%29%2Fln%282%29
using the calc
-t%2F5.7 = -1.32193
t = -5.7 * -1.32193
t = +7.535 ~ 7.5 hrs to decay to 80 mg