A student has 3 hours to cram for an examination and during this time wishes to memorize a set of 60 items. It is said that the rate at which a person can memorize a set of items is proportional to the number of items remaining to be memorized. Thus, if the student memorizes y items in t minutes, dy = k(60 – y) dt where k is a positive constant and y < 60 for all t. Assume that zero items are memorized initially and the student memorizes 15 items in the first 20 minutes. A. Express y as a function of t. B. How many items can the student memorize in 1 hour? in 3 hours?

The rate of U.S. per capita sales of bottled water for the period 1993-2003 could be approximated by Q(t) = 0.05r +0.41 +9 where t is the time in years since 1990. Compute the average annual sales of bottled water over the period 1996-2003, to the nearest gallon per year. O a. 15 gallons per year b. 17 gallons per year O c. 16 gallons per year O d. 18 gallons per year е. 19 gallons per year

A tank contains 1000-gallon of pure water. Starting at time t = 0, a solution containing 0.2 lb of salt per gallon enters 10 gallons per minute and the well-stirred solution is withdrawn at a rate of 5 gallons per minute. Set up the initial value problem for the amount of salt, Q(t), in the tank as a function of t. Sove for Q(t).