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. Write the differential equation satisfied by y in terms of a proportionality factor k. (Express numbers in exact form. Use symbolic notation and fractions where needed.) y (t) = Find k (in units of day-), assuming that 15% of the population knows the rumor at t = 0 and 35% knows it at t = 2 days. (Express numbers in exact form. Use symbolic notation and fractions where needed.) k = days-
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. Write the differential equation satisfied by y in terms of a proportionality factor k. (Express numbers in exact form. Use symbolic notation and fractions where needed.) y (t) = Find k (in units of day-), assuming that 15% of the population knows the rumor at t = 0 and 35% knows it at t = 2 days. (Express numbers in exact form. Use symbolic notation and fractions where needed.) k = days-
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text: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.
Write the differential equation satisfied by y in terms of a proportionality factor k.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
y (t) =
Find k (in units of day-), assuming that 15% of the population knows the rumor at t = 0 and 35% knows it at t = 2 days.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
k =
days-1
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