Sociologists model the spread of rumors using logistic equations. The key assumption is that at any given time a fraction y of the population, where 0sys1 the rumor, while the remaining fraction 1-y does not. Furthermore, the rumor spreads by interactions between those who know the rumor and those who de number of such interactions is proportional to y(1-y). Therefore, the equation that describes the spread of the rumor is y'(t) = ky(1-y), where k is a positive number. The fraction of people who initially know the rumor is y(0) = yo, where 0sy, s1. Complete parts (a) to (c) below. ..... a. Solve this initial value problem and give the solution in terms of k and yo- Start by writing y'(t) = ky(1-y) in separated form. dy = kdt y(1-y) ook Integrate both sides. y In 1-y, = kt +C (Do not simplify.) ents Raise e to the power of each side of the equation. y cess 1-y Library Taka the recinrocal of each sirla of the eauation otions Textbook Print Clear all Check answ tesourc

Sociologists model the spread of rumors using logistic equations. The key assumption is that at any given time a fraction y of the population, where 0sys1 the rumor, while the remaining fraction 1-y does not. Furthermore, the rumor spreads by interactions between those who know the rumor and those who de number of such interactions is proportional to y(1-y). Therefore, the equation that describes the spread of the rumor is y'(t) = ky(1-y), where k is a positive number. The fraction of people who initially know the rumor is y(0) = yo, where 0sy, s1. Complete parts (a) to (c) below. ..... a. Solve this initial value problem and give the solution in terms of k and yo- Start by writing y'(t) = ky(1-y) in separated form. dy = kdt y(1-y) ook Integrate both sides. y In 1-y, = kt +C (Do not simplify.) ents Raise e to the power of each side of the equation. y cess 1-y Library Taka the recinrocal of each sirla of the eauation otions Textbook Print Clear all Check answ tesourc

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 2TI: Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time...

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