test_102910_sol - Midterm 1:10-2:00pm Matt Turner You have...

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EC314-Fall 2010 Midterm 1:10-2:00pm, October 29, 2009 Matt Turner You have 50 minutes to complete this exam. Anyone still working on their exam after this time expires is subject to an automatic penalty of not less than 5 points. No notes or books are allowed, but you may use a calculator. All cell phones and pagers must be off. When you write up your answers, your goal should be to (1) be correct, and (2) convince your reader that your answer is correct. Answers which do not achieve these goals will not be awarded full credit. To accomplish the second objective, it is helpful if your work is legible and if all steps are presented, possibly with a line of explanation. Total points =100/ Share of total mark=35%. 1. (30) Let the stock of water in the aquifer at a given time be denoted by x ( t ) > 0 and suppose that water recharges the aquifer as a function of the stock level according to F ( x ) = 20 x ( 1 - x ) (a) What is the stock level that maximizes the recharge rate?
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