Math 1206 Workshop #3 due Monday Feb. 4, 2013 at the beginning of your workshop

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Math 1206 Workshop #3 due Monday Feb. 4, 2013 at the beginning of your workshop Consider a lunar colony with a population of 200, 000 people. A highly infectious incurable disease breaks out in the colony and they are isolated from all other humans. Initially. 1300 people are infected and the initial infection rate is 497 people per day. A mathematical model for the infection rate of this disease dn/dt = kN(200 - N): where N = N(t) is the number of people infected and kappa is a constant to be determined. Explain why this model may be suitable to model the infection rate of this disease. Using the information in the problem, find a value of kappa for this model. Using your answer in (2). solve the differential equation (A) by integrating both sides of: and solving for N = N(t). Verify that the function N you found in part (3) is indeed a solution of equation (A) using differentiation. Using your answer in (3), find the number of people you expect to be infected after 4 days.

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