SOLUTION: A cup of coffee contains 130 milligrams of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how long will it take for 90% of this caffeine to be elimina

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Question 1189644: A cup of coffee contains 130 milligrams of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how long will it take for 90% of this caffeine to be eliminated from a person's body
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
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A cup of coffee contains 130 milligrams of caffeine.
If caffeine is eliminated from the body at a rate of 11% per hour,
how long will it take for 90% of this caffeine to be eliminated from a person's body
~~~~~~~~~~~~~~~~

The decay equation is

    M(t) =  = .


To solve, divide both sides by 130

    0.1 = 


and take logarithm base 10 of both sides.  We get then

    log(0.1) = t*log(0.89)


and find 

    t =  = 19.76 hours.    ANSWER


CHECK.  The remaining mass is  M(19.76) =  = 13.9984 milligrams, 

        which is a good precision, comparing with 13 milligrams.

Solved.



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