Problem Set 3 1. A tank contains 1000 gallons of brine with 15 lbs of dissolved salt. Pure water enters the tank at a rate of 10 gal/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes? 2. A 500 gal tank contains 200 gal of water with 100 lb salt. Water containing 1lb salt per gallon enters at 3 gal/min. the mixture leaves at 2 gal/min. What is the amount of salt, and the concentration, after t minutes? When will you get overflow, and what is the concentration at that time? 3. You graduate from UT, get a job, and borrow $8000 to buy a car. The lender charges interest at a rate of 10% annually. Assuming that interest is compounded continuously and that you’re making payments continuously at a constant annual rate k, determine the k needed so that you can pay off the car loan in 3 years. 4. A ball with mass 0.15 kg is thrown upward with initial velocity 20 m/sec from the roof of a building 30 m high. When will the ball hit the ground and how fast will it be going at that time? When and where
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