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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 0syo s1. Complete parts (a) to (c) below. ......

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 0syo s1. Complete parts (a) to (c) below. ......

College Algebra
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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Can someone tell me why my answer is wrong??!! The part says substitute 0 for t. Separable Differential Equations
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. ..... ook Start by writing y'(t) = ky(1 - y) in separated form. 1. dy = kdt y(1-y) ents Integrate both sides. cess In 1-y = kt +C (Do not simplify.) Library Raise e to the power of each side of the equation. ptions y = ekt.c 1-y Resourc Take the reciprocal of each side of the equation. pols Textbook Print Clear all Check answer TIS Course IMATT ZZr ratzuzTIS Das ranCartuius gentais, Je ENG 11/ DELL F2 F3 FS F4 F6 FZ F9 F10 F11 F12 PriScr Insert Delete %23 9 Backspa E R T Y P D F H J K L C B M Alt Alt Ctr
Transcribed Image Text: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. ..... ook Start by writing y'(t) = ky(1 - y) in separated form. 1. dy = kdt y(1-y) ents Integrate both sides. cess In 1-y = kt +C (Do not simplify.) Library Raise e to the power of each side of the equation. ptions y = ekt.c 1-y Resourc Take the reciprocal of each side of the equation. pols Textbook Print Clear all Check answer TIS Course IMATT ZZr ratzuzTIS Das ranCartuius gentais, Je ENG 11/ DELL F2 F3 FS F4 F6 FZ F9 F10 F11 F12 PriScr Insert Delete %23 9 Backspa E R T Y P D F H J K L C B M Alt Alt Ctr
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. -= e kt.C 1-y Take the reciprocal of each side of the equation. 1-y - kt. C Solve for y. y = - kt. eC + 1 e Substitute 0 for t and y, for y to find C. C= log 1 -1 (Simplify your answer.) Textbook Print Clear all Check answer ENG DELL F7 F10 F9 F11 Priscr Ins F12 %23 24 2 3 4 5 6 Y F H K L C M >
Transcribed Image Text: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. -= e kt.C 1-y Take the reciprocal of each side of the equation. 1-y - kt. C Solve for y. y = - kt. eC + 1 e Substitute 0 for t and y, for y to find C. C= log 1 -1 (Simplify your answer.) Textbook Print Clear all Check answer ENG DELL F7 F10 F9 F11 Priscr Ins F12 %23 24 2 3 4 5 6 Y F H K L C M >
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