A rumor spreads through a school. 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 y that has not yet heard the rumor. has heard the rumor and the fraction 1 The school has 1000 students in total. At 8 a.m., 107 students have heard the rumor, and by noon, half the school has heard it. Using the logistic model explained above, determine how much time passes before 90% of the students will have heard the rumor. hours. 90% of the students have heard the rumor after about

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.7: Applications
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A rumor spreads through a school. 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
y that has not yet heard the rumor.
has heard the rumor and the fraction 1
The school has 1000 students in total. At 8 a.m., 107 students have heard the rumor, and by noon, half the school
has heard it. Using the logistic model explained above, determine how much time passes before 90% of the
students will have heard the rumor.
hours.
90% of the students have heard the rumor after about
Transcribed Image Text:A rumor spreads through a school. 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 y that has not yet heard the rumor. has heard the rumor and the fraction 1 The school has 1000 students in total. At 8 a.m., 107 students have heard the rumor, and by noon, half the school has heard it. Using the logistic model explained above, determine how much time passes before 90% of the students will have heard the rumor. hours. 90% of the students have heard the rumor after about
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