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) = Yo, where 0sy, s1. Complete parts (a) to (c) below. 0.3 and graph the solution for yo = 0.3 and yo = 0.7. Which of the following graphs shows the solution for y, =0.3 b. Assume k= 0.3 weeks which means weeks in blue (the lower plot) and the solution for yo =0.7 in red (the upper plot)? OA. VB. C. OD. rary Q Q Q ons sourd 04 0. 0- 30 0+ 0- 30 30 c. Describe and interpret the long-term behavior of the rumor function for any 0s Yo $1. For any 0sy, s1. lim y(t) = (Type an integer or a simplified fraction.) t-00 Textbook Print Clear all Check answer

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) = Yo, where 0sy, s1. Complete parts (a) to (c) below. 0.3 and graph the solution for yo = 0.3 and yo = 0.7. Which of the following graphs shows the solution for y, =0.3 b. Assume k= 0.3 weeks which means weeks in blue (the lower plot) and the solution for yo =0.7 in red (the upper plot)? OA. VB. C. OD. rary Q Q Q ons sourd 04 0. 0- 30 0+ 0- 30 30 c. Describe and interpret the long-term behavior of the rumor function for any 0s Yo $1. For any 0sy, s1. lim y(t) = (Type an integer or a simplified fraction.) t-00 Textbook Print Clear all Check answer

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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