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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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) About Me  (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
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The decay equation is

    M(t) = 130%2A%281-0.11%29%5Et = .


To solve, divide both sides by 130

    0.1 = 0.89%5Et


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

    log(0.1) = t*log(0.89)


and find 

    t = log%28%280.1%29%29%2Flog%28%280.89%29%29 = 19.76 hours.    ANSWER


CHECK.  The remaining mass is  M(19.76) = 130%2A0.89%5E19.76 = 13.9984 milligrams, 

        which is a good precision, comparing with 13 milligrams.

Solved.