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Homework-4-s12

# Homework-4-s12 - ࠵ The resistance in Medium-1 is ࠵ ࠵...

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Homework 4 Assignment Date: Wednesday (02/08/2012) Collection Date: Wednesday (03/07/2012) Grade: Each problem is worth 10 points Problem 4.1: Solve the following DE using two methods considered in Chapter 1: 1 + 2 ࠵± = 1 + 2 Problem 4.2: Solve the following DE using two methods considered in Chapter 1: + ! = 1 Problem 4.3: Consider a prolific animal whose birth and death rates, and , are each proportional to its population with > and ! = = 0 . (a) Compute the population as a function of time and parameters and initial condition given; (b) Find the time for doomsday; (c) Suppose that ! = 100 and that there are 270 animals after 12 months, when is the doomsday? (d) If < , compute the population limit when time approaches infinity? Problem 4.4: Consider shooting a bullet of mass to three connected (and fixed) media each of equal length
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Unformatted text preview: ࠵ . The resistance in Medium-1 is ࠵ ࠵ ! , in Meduim-2 is ࠵ ࠵ ! , and in Medium-3 is ࠵ ࠵ ! . Compute the bullet’s speed to enter Medium-1 such that the bullet will pass through Medum-1 and then Medium-2, and then Medium-3, and magically stop precisely at the edge of Medium-3. You may neglect gravity. Problem 4.5: Suppose that the fish population ࠵ ( ࠵ ) in a lake is attacked by a disease (such as human being who eats them) at time ࠵ = , with the result that the fish cease to reproduce (so that the birth rate is ࠵ = ) and the death rate ࠵ (deaths per week per fish) is thereafter proportional to ࠵ ! ! ! . If there were initially 999 fish in the lake and 66 were left after 16 weeks, how long did it take all the fish in the lake to die? Can you change the “66” to a different number such that the fish count never changes with time? To what number if so?...
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