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, knows 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 do not. The 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 real number. The fraction of people who initially know the rumor is y(0) = y0, where 0sy, s1. Complete parts (a) to (c) below. ...... Solve for y. -kt Substitute 0 for t and y, for y to find C. rary 1-Yo ons C= In Yo (Simplify your answer.) sourc Substitute C back into the found general solution. (Simplify your answer.) yo-1 1- kt e yo Textbook Print Clear all Final check 10:56

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, knows 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 do not. The 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 real number. The fraction of people who initially know the rumor is y(0) = y0, where 0sy, s1. Complete parts (a) to (c) below. ...... Solve for y. -kt Substitute 0 for t and y, for y to find C. rary 1-Yo ons C= In Yo (Simplify your answer.) sourc Substitute C back into the found general solution. (Simplify your answer.) yo-1 1- kt e yo Textbook Print Clear all Final check 10:56

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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