A 750 gallon tank starts off containing 400 gallons of water and 30 pounds of salt. Water with a salt concentration of 0.5 pounds/gallon is added to the tank at a rate of 4 gallons per minute. At the same time, water is removed from the well-mixed tank at a rate of 7 gallons per minute. a. Write and solve an initial value problem for the volume V(t) of water in the tank at any time t. b. Set up an initial value problem for Q(t), the amount of salt (in pounds) in the tank at any time t. Solving the problem is not necessary, but please include the entire problem definition. c. Even though you have not solved the problem for part (b), will the function Q(t) that you would solve for make sense for describing the physical tank for all positive t values? If so, determine the long term behavior as t approaches infinity. If not, determine the value for t when the connection between the tank and the equation breaks down, as well as what happens physically at this point in time. Please solve parts a, b, and c.
A 750 gallon tank starts off containing 400 gallons of water and 30 pounds of salt. Water with a salt concentration of 0.5 pounds/gallon is added to the tank at a rate of 4 gallons per minute. At the same time, water is removed from the well-mixed tank at a rate of 7 gallons per minute.
a. Write and solve an initial value problem for the volume V(t) of water in the tank at any time t.
b. Set up an initial value problem for Q(t), the amount of salt (in pounds) in the tank at any time t. Solving the problem is not necessary, but please include the entire problem definition.
c. Even though you have not solved the problem for part (b), will the function Q(t) that you would solve for make sense for describing the physical tank for all positive t values? If so, determine the long term behavior as t approaches infinity. If not, determine the value for t when the connection between the tank and the equation breaks down, as well as what happens physically at this point in time.
Please solve parts a, b, and c.
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