- #1

oneamp

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## Homework Statement

Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 L / min. The well stirred solution flowing out at the same rate. Find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value.

## Homework Equations

This is my first differential equations word problem, so I'm trying to learn how to do them. I don't need the answer to the 1% question; just some advice on what I did wrong below.

## The Attempt at a Solution

[itex]

\frac{dQ}{dt} = -(\frac{2L}{min})(\frac{Q(t)}{200L}) = \frac{-1}{2} Q(t)

[/itex]

Initial value: Q(0) = 1g/L

[itex]

\frac{dQ}{dt} + \frac{1}{2} Q = 0

[/itex]

[itex]

\mu = e^{1/2*t}

[/itex]

[itex]

Q(t) = \frac{C}{e^{1/2*t}}

[/itex]

At this point I solve for C using the initial value, and get Q(t) = 1 :( Where am I going wrong?

Thank you