p1spring10 pages 1 to 6 - Prelim 1 Math 2930 Spring 2010...

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Unformatted text preview: Prelim 1 Math 2930 Spring 2010 show work, 6 problems, no calculators 1a) (4 points) Write your name and section number at the top of this page. 1b) (4 points) The chef wants to put a 100C dish into a 200C oven at time 0, and he thinks the temperature T ( t ) of the dish will evolve according to T = 1 20 ( T- 200) But he made a mistake: Explain why there ought to be a minus sign on the 1 20 coefficient. 1c) (12 points) Solve the corrected equation T =- 1 20 ( T- 200) using the chefs initial condition. 1 2) A population p ( t ) [thousands] is described by the differential equation p ( t ) = 1 10 p ( t )- 1 1000 ( p ( t )) 3 a) (4 points) Find three equilibrium (constant) solutions. b) (6 points) Determine the stability of the positive equilibrium. c) (6 points) Use two steps of Eulers numerical method to estimate the population at time t = 0 . 2, if we assume p (0) = 3 . 0. You should find the approximations p and p 1 exactly, but you do not have to simplify the ex- pression for p 2 ....
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This note was uploaded on 01/21/2011 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).

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p1spring10 pages 1 to 6 - Prelim 1 Math 2930 Spring 2010...

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