REVIEW PROBLEMS FOR MIDTERM II MATH 2574H, SPRING 2012 Summary: ANSWER KEY REVIEW PROBLEMS FOR MIDTERM II MATH 2574H, SPRING 2012 UNIVERSITY OF MINNESOTA This is a selection of problems meant to be reasonable practice for the upcoming exam. These problems (or portions thereof) are possible types of exam questions. Please note that the usual disclaimer continues to apply, namely, this is not guar- anteed to be an absolutely complete review. To be perfectly ready you have to have a grip on all the homework that has been assigned in weeks 4,5,6,7. Salt tank problem A tank has a huge capacity, so huge we will not worry about the possibility of overflow. At time t = 0 the tank contains 64 gallons of water with 10 pounds of the top secret ingredient of Calca-Cola dissolved in the water. Then solution containing 1 pound of secret ingredient per gallon of water is allowed to flow into the tank at a rate of 5 gallons per minute. Simultaneously, well-mixed solution is allowed to drain out of the tank at a rate of 1 gallon per minute. Find a formula for the amount of secret ingredient in the tank at time t. Show all your work. Solution Let S = S(t) be the amount of secret ingredient in the tank at time t. The initial value problem we have to solve is the following: Collections: Mathematics