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Answer:
Step-by-step explanation:
The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.
Volume = 500 gallons
Initial Amount of Salt, A(0)=50 pounds
Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min
=(concentration of salt in inflow)(input rate of brine)
When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.
Concentration c(t) of the salt in the tank at time t
Concentration,
=(concentration of salt in outflow)(output rate of brine)
Now, the rate of change of the amount of salt in the tank
We solve the resulting differential equation by separation of variables.
Taking the integral of both sides
Recall that when t=0, A(t)=50 (our initial condition)