Differential equations chemical solutions problem

[4102]

Homework Statement

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

Homework Equations

dx/dt + F_o (x)/V_o = F_iC_i

The Attempt at a Solution

I used the equation above. Where:

F_o=3cm³/sec
Vo=125cm³
F_i=3
C_i=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 = x_o e^(-3t/125)

but i can't seem to arrive at .2(1-e^(-3t/125))

 

[hunt_mat]

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.

 

[4102]

I finally solved it

Instead of assuming C_i = 0, i substituted .2

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

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

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

Thank you very much!