Differential Equation Model help please

[caseclosed]

This is from the book, need help changing it into mathematical model.

 

"Consider a tank used for certain hydrodynamic experiments. After one experiment the tank contains 200 litres of a dye solution with a concentration of 1 g/litre. To prepare for the next experiment, the tank is rinsed with fresh water flowing in at a rate of 2 litres/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 readches 1% of its original value."

[Bignose]

Consider a balance around the tank. The only way the amount of dye can change over time is if dye flows in, flows out, or is created or destroyed (like via a chemical reaction).

 

In words, this looks like:

 

Change in amount of dye per unit time =

Amount of dye that flows in per unit time

-Amount of dye the flows out per unit time

+Amount of dye created per unit time

-Amount of dye consumed (or destroyed) per unit time.

 

I've written the necessary equation in words, you should be able to write the equation in symbols now.

[casperl]

Consider a balance around the tank. The only way the amount of dye can change over time is if dye flows in, flows out, or is created or destroyed (like via a chemical reaction).

 

In words, this looks like:

 

Change in amount of dye per unit time =

Amount of dye that flows in per unit time

-Amount of dye the flows out per unit time

+Amount of dye created per unit time

-Amount of dye consumed (or destroyed) per unit time.

 

I've written the necessary equation in words, you should be able to write the equation in symbols now.

 

Good explanation.