Answer:
dA / dt = 6 - A (t) / 100
600
Step-by-step explanation:
We have to:
dA / dt = In - Out
Input = input salt concentration * input rate of brine
replacing
Inlet = 2 lb / gal * 3 gal / min = 6 lb / min
there is no build up because the inlet flow equals the outlet, so there are 300 gallons in the tank at the start
Output: salt concentration at the output * output rate of brine
replacing
Output: A (t) / 300 * 3 gal / min = A (t) / 100
Thus:
dA / dt = 6 - A (t) / 100
this would be the differential equation.
now, when time tends to infinity, we would be left with:
100 * dA / dt = 600 - A (t)
When t tends to infinity, A (t) tends to 0, therefore, the amount of salt would be 600.
