A tank with a capacity of 100 gallons initially contains 50 gallons of water with 10 pounds of salt in solution. fresh water enters at a rate of 2 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. compute the amount of salt (in pounds) in the tank at the first moment when the tank is filled.
Accepted Solution
A:
Let [tex]A(t)[/tex] be the amount of salt (in pounds) in the tank at time [tex]t[/tex]. We're given that[tex]A(0)=10\text{ lb}[/tex].
The rate at which the amount of salt in the tank changes is given by the ODE