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A college dormitory houses 100 students, each of whom is susceptible to a certain virus infection. A simple model of epidemics assumes that during the course of an epidemic the rate of change with respect to time of the number of infected students, I is proportional to the number of infected students and is also proportional to the number of uninfected students, 100 – I. a. If the time t = 0 a single student becomes infected, show that the number of infected students at time t is given by 100e100kt 99 + e100kt b. 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 9 days.

A college dormitory houses 100 students, each of whom is susceptible to a certain virus infection. A simple model of epidemics assumes that during the course of an epidemic the rate of change with respect to time of the number of infected students, I is proportional to the number of infected students and is also proportional to the number of uninfected students, 100 – I. a. If the time t = 0 a single student becomes infected, show that the number of infected students at time t is given by 100e100kt 99 + e100kt b. 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 9 days.

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A college dormitory houses 100 students, each of whom is susceptible to a certain virus infection. A simple model of epidemics assumes that during the course of an epidemic the rate of change with respect to time of the number of infected students, I is proportional to the number of infected students and is also proportional to the number of uninfected students, 100 – I. If the time t = 0 a single student becomes infected, show that the number of infected students at time t is given by 100e100kt I 99 + e100kt b. 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 9 days.
Transcribed Image Text:A college dormitory houses 100 students, each of whom is susceptible to a certain virus infection. A simple model of epidemics assumes that during the course of an epidemic the rate of change with respect to time of the number of infected students, I is proportional to the number of infected students and is also proportional to the number of uninfected students, 100 – I. If the time t = 0 a single student becomes infected, show that the number of infected students at time t is given by 100e100kt I 99 + e100kt b. 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 9 days.
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