A rumor spreads through a small town. Let y(t) be the fraction of the population that has
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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.
(a) Write the differential equation satisfied by y in terms of a proportionality factor k.
(b) 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.
(c) Using the assumptions of part (b), determine when 75% of the population will know the rumor.
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a y t is the rate at which the rumor is spreading in percentage of the population p...View the full answer
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