A tank initially contains 150 gal of brine in which 20lb of salt are dissolved. A...

A tank initially contains 150 gal of brine in which 20lb of salt are dissolved. A brine containing 3 lb/gal of salt runs into the tank at the rate of 4 gal/min.The mixture is kept uniform by stirring and flows out of the tank at the rate of 3 gal/min. Let y represent the amount of salt at time t. Complete parts a through e.

a. At what rate (pounds per minute) does salt enter the tank at time t?

b. What is the volume of brine in the tank at time t?

c. At what rate (pounds per minute) does salt leave the tank at time t?

d.Write down and solve the initial value problem describing the mixing process. What is the solution to the initial value problem?

e. Find the concentration of salt in the tank 28 min after the process starts.

Solutions

Expert Solution

Colby Messinger answered 6 months ago

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