A rumor spreads through a small town. Let y(t)be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1-y that has not yet heard the rumor. 1. Write down the differential equation satisfied by y in terms of a proportionality factor k. 2. Find k (in units of day-1), assuming that 10% of the population knows the rumor at t=0 and 40% knows it at t=2 days. 3. Using the assumptions of part (b), determine when 75% of the population will know the rumor.
A rumor spreads through a small town. Let y(t)be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1-y that has not yet heard the rumor.
1. Write down the differential equation satisfied by y in terms of a
proportionality factor k.
2. Find k (in units of day-1), assuming that 10% of the population
knows the rumor at t=0 and 40% knows it at t=2 days.
3. Using the assumptions of part (b), determine when 75% of the
population will know the rumor.
y denotes the fraction of population who have heard the rumour then 1 minus y represents the fraction of population who haven't heard the rumours.
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