Answer:
The amount of salt in the tank at any time t is
Explanation:
By definition, we have that the change rate of salt in the tank is , where is the rate of salt entering and is the rate of salt going outside.
Then we have, , and
So we obtain. , then
, and using the integrating factor , therefore
, we get , after integrating both sides , therefore , to find we know that the tank initially contains 120L of pure water, that means the initial conditions , so
Finally we can write an expression in terms of γγ for the amount of salt in the tank at any time t, it is