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MT_1_Math_33B_W09

# MT_1_Math_33B_W09 - Mathematics 33B Midterm 1 January 30th...

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Mathematics 33B - Midterm 1 January 30th, 2009 Instructor: D.E.Weisbart NAME (please print legibly): Your University ID Number: Your Discussion Section and TA: Signature: Calculators, notes and books may not be used in this examination. You may not receive full credit for a correct answer if insuﬃcient work is shown. QUESTION VALUE SCORE 1 20 2 20 3 20 4 20 5 20 TOTAL 100 1

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1. (20 points) The equation P 0 = P (4 - P ) - 3 is a model for the growth of a population which is harvested. Find the equilibrium solutions to this equation and determine whether they are asymptotically stable or unstable. 2
A tank contains 40 gallons of pure water. Starting at time zero, a salt-water solution containing 0.5 lb/gal of salt enters the tank at a rate of 2 gal/min. At the same time a drain is opened at the bottom of the tank allowing the salt-water solution to leave at a rate of 2 gal/min. Assume that the solution is kept perfectly mixed at all times. How long will it take for the amount of salt in the tank to reach 5 lbs? Leave your answer in exact form (in terms of logarithms). 3

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MT_1_Math_33B_W09 - Mathematics 33B Midterm 1 January 30th...

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