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

Question

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

turingtest · Answer

|dw:1346951512741:dw|

turingtest · Answer

Q(t) is the amount of substance in the tank. Because the inflow is clean water the rate at which Q(t) enters the tank is zero.
The rate at which Q(t) leaves the tank is|dw:1346951732985:dw|

turingtest · Answer

this is separable, and using the initial value of Q(0)=1(g/L) we can get a particular solution to this IVP