Assignment 5

Assignment 5 - Math 138 Assignment 5 Fall 2008 The...

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Unformatted text preview: Math 138 Assignment 5 Fall 2008 The following questions are to be answered neatly and completely on standard size (8.5 by 11 inch, or metric equivalent) paper. Please insure that your name and ID number are clearly indicated on each page, and that all your pages are securely fastened together, staples are preferred. This assignment is due at 9:00 a.m. on Friday, October 24, 2008 . 1. Biologists stocked a lake with 400 fish and estimated the carrying capacity (the maximum population for the fish of that species in the lake) to be 10 000. The number of fish tripled in the first year. a) Assuming that the size of the fish population satisfies the logistic equation (see page 592 of the text), find an expression for the size of the population after t years. b) How long will it take for the population to increase to 5000? 2. a) Use Eulers method with step-size 0.2 to estimate y (0 . 4) where y ( x ) is the solution to the initial- value problem: y = 2 xy 2 y (0) = 1 b) Repeat part (a) with step-size 0.1.b) Repeat part (a) with step-size 0....
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