A college dormitory houses 100 students, each of whom is susceptible to a certain virus infection. A simple model of epidemic assumes that during the course on an epidemic, the rate of change on the number of infected students (1) with respect to time is directly proportional to the number of infected students (I) and also directly proportional to the number of uninfected students (100-1). If at time t = 0 a single student becomes infected, determine the following:

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