Question 1189644
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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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<pre>
The decay equation is

    M(t) = {{{130*(1-0.11)^t}}} = {{{130*0.89^t}},

where M(t) is the remaining mass of the caffeine in the body, in milligrams; t is the time, in hours.


When 90% of the caffeine eliminated, 10% remained, or 13 milligrams.  So we write

    13 = {{{130*0.89^t}}}.


To solve, divide both sides by 130

    0.1 = {{{0.89^t}}}


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

    log(0.1) = t*log(0.89)


and find 

    t = {{{log((0.1))/log((0.89))}}} = 19.76 hours.    <U>ANSWER</U>


<U>CHECK</U>.  The remaining mass is  M(19.76) = {{{130*0.89^19.76}}} = 13.9984 milligrams, 

        which is a good precision, comparing with 13 milligrams.
</pre>

Solved.