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Homework Help: Differential equations chemical solutions problem

  1. Jul 10, 2010 #1
    1. The problem statement, all variables and given/known data
    newbie here..

    Blood carries a drug into an organ at the rate of 3 cm^3/sec and leaves at the same rate. The organ has a liquid volume of 125 cm^3. If the concentration of the drug in the blood entering the organ is .2g/cm^3, what is the concentration of the drug in the organ at time t? After how many seconds will the concentration the drug in the organ reach 0.1g/cm^3?

    Answer should be .2(1-e(-3t/125)) and 28.9 seconds



    2. Relevant equations

    dx/dt + Fo (x)/Vo = FiCi

    3. The attempt at a solution

    I used the equation above. Where:

    Fo=3cm3/sec
    Vo=125cm3
    Fi=3
    Ci=0

    I'm really not sure if I'm doing it right, because i just based on my teacher's previous solutions on other problems

    i end up at x = xo e(-3t/125)

    but i can't seem to arrive at .2(1-e(-3t/125))
     
    Last edited: Jul 10, 2010
  2. jcsd
  3. Jul 10, 2010 #2

    hunt_mat

    User Avatar
    Homework Helper

    I think it's in your assumption of C_{i}=0 that messes things up. Check to make sure that this is indeed the case.
     
  4. Jul 11, 2010 #3
    I finally solved it

    Instead of assuming Ci = 0, i substituted .2

    then I have
    [tex]
    \frac{dx}{dt} + \frac{3x}{125} = (3)(.2)
    [/tex]
    I used linear differential equation
    [tex]
    v=e^{\int\frac{3}{125} dt} = e^{\frac{3t}{125}}
    [/tex]
    then
    [tex]
    xe^{\frac{3t}{125}} = \int(.6)(e^{\frac{3t}{125}}) dt + C
    [/tex]

    then I looked for the value of C which is -.2 and substituted it into the equation

    then I finally got [tex] x=.2(1-e^{\frac{-3t}{125}}) [/tex]

    Thank you very much!
     
    Last edited: Jul 11, 2010
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