Answer:
The amounts of salt in the tank at any time prior to the instant when the solution begins to overflow is.
Step-by-step explanation:
Let Q(t) be the amount of salt in the tank at any time .
Then, its time of change, by (Balance law).
Since three gallons of salt water runs in the tank per minute, containing lb of salt, the salt inflow rate is
The amount of water in the tank at any time is,
Now, the outflow is gal of the solution in a minute. That is of the total solution content in the tank, hence of the salt salt content , that is ,
Initially, the tank contains lb of salt,
Therefore, we obtain the initial condition
Thus, the model is
here, Linear ODE
So, the integrating factor is
and the general solution is
using initial condition and find the value of constant c.
Hence, is the amount of salt in the tank at any moment t.