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Exponential problem: caffeine dosage

  1. Mar 23, 2013 #1
    If the concentration of caffeine in a system at any given time is given by the equation
    where dy/dt=-kt is the clearence rate (re-arranged and integrated to form the above equation) and the concentration of caffeine in the system at t=0 is D, then calculate k if:
    After one hour, 25% of the caffein has been cleared.

    I know that y(60)= 3D/4 or three quarters of D
    so how do I re-arrange to get k?
  2. jcsd
  3. Mar 23, 2013 #2


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    y(60)=De^(-k*60). That's equal to 3D/4. It shouldn't be too hard to solve for k if you use a log, is it?
  4. Mar 23, 2013 #3
    OH! I see now. Just subtitute in 3/4D for y(60) then divide by D, take ln of both sides and divide by negative 60. Thank you!
  5. Mar 23, 2013 #4

    Ray Vickson

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    Note: dy/dt is NOT equal to -kt; it is equal to -ky.
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