A p p l i c a t i o n s : D e c o m p o s i t i o n / G r o w t h and N e w t o n ’ s L a w of C o o l i n g A6.2 A college dormitory houses 100 students, each of whom is susceptible to a certain virusinfection. A simple model of epidemics assumes that during the course of an epidemic therate of change with respect to time of the number of infected students, I is proportional tothe number of infected students and is also proportional to the number of uninfectedstudents, 100 – I.If the time t = 0 a single student becomes infected, show that the number ofinfected students at time t is given by100e100ktI99 + e100ktb. If the constant of proportionality k has a value 0.01 when t is measured in days,find the value of the rate of new cases l'(t) at the end of each day for the first 9days.

Given: At t = 0, the number of an infected person is I = 1 The total number of the student is 100

Answered: A college dormitory houses 100…

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