MA1014_HW5r_201012

MA1014_HW5r_201012 - Mathematics for Engineering 2 Homework...

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Mathematics for Engineering 2 Homework 5: Differential Equations [email protected] Solve the following problems: 1. A group of sociologists studied the average annual income (in US dollars) of people from a particular urban group. In particular, they focused on the income y as a function of the number of years of education x , when considering a standard job. They found that the rate of change of income with respect to education is given by dy dx = 100 x 3 2 ;4 x 16 , where y = \$ 28720 when x = 9. Find y . 2. A glucose solution is administered intravenously into the bloodstream at a constant rate r . As the glucose is added, it is converted into other substances and removed from the bloodstream at a rate that is proportional to the concentration at that time. Thus a model for the concentration C = C ( t ) of the glucose solution in the bloodstream is dC dt = r kC where k is a positive constant. Suppose that the concentration at time t = 0 is C 0 .

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