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Answer:
Step-by-step explanation:
concentration = amount of salt/solution
A) Initial concentration= 90/1000 = 0.09
Q = quantity of salt
Q(0) = 90 kg
Inflow rate = 8 l/min
Outflow rate = 8 l/min
Solution = 1000 L at any time t.
Salt inflow = 0.045 * 8 per minute
= 0.36 kg per minute
This is mixed and drains from the tank.
Outflow =
Thus rate of change of salt
Q'(t) = inflow - outflow =
Separate the variables and integrate
Use the fact that Q(0) = 90
90 = 360-A
A = 270
So
B) Q(t) = 360-270e^-0.004 = 91.07784
C) When t approaches infinity, we get
Q(t) tends to 360
So concentration =360/1000 = 0.36