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Unformatted text preview: 18.03 Problem Set 9 Fall 2009 Solutions 1. (25 points) There are three kinds of people in the world: students, professors, and workers. Let us denote the population of each kind at time t by S ( t ) = number of students at time t, W ( t ) = number of workers at time t, P ( t ) = number of professors at time t. These numbers are governed by a system of differential equations: dS dt = 1 4 S ( t ) + 1 48 W ( t ) dW dt = 6 25 S ( t ) 1 50 W ( t ) dP dt = 1 100 S ( t ) 1 50 P ( t ) . ( System of ODE ) The first equation says that one fourth of the students graduate each year, and are replaced by reproduction of the workers; a worker produces one student each 48 years. In this model the professors do not reproduce. The second equation says that 96% of the graduating students become workers, and that one fiftieth of the workers die each each year. The third equation says that 4% of the graduating students become professors, and that one fiftieth of the professors die each year. a) (5 points). The equation (System of ODE) says that you can study just S ( t ) and W ( t ) without caring at all about P ( t ) . (The reason is that P ( t ) does not appear in the differential equations for...
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This note was uploaded on 05/06/2010 for the course 18 18.03 taught by Professor Unknown during the Spring '09 term at MIT.
 Spring '09
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