Question 4: 20 Marks The monkeypox virus is spreading in a small village with a population size of 5000 inhabitants. Ini

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Question 4 20 Marks The Monkeypox Virus Is Spreading In A Small Village With A Population Size Of 5000 Inhabitants Ini 1 (36.75 KiB) Viewed 29 times

Question 4: 20 Marks The monkeypox virus is spreading in a small village with a population size of 5000 inhabitants. Initially only one inhabitant has the monkeypox. Let us assume that the rate at which inhabitants contract the monkeypox virus is directly proportional to the number of inhabitants who are already infected. Let M (t) represent the number of inhabitants who have the monkeypox after t days. (4.1) Write down the differential equation for the variable M. (4.2) After 3 days, 10 inhabitants have the monkeypox virus. How many inhabitants will have the monkeypox after 12 days? (4.3) Plot the phase line of the model. (4.4) Determine the rate of change of M at t = 0, t = 3 and t = 12. (4.5) Utilize all the information available to plot the solution curve M (t).