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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. Th 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 s 1. 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.

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. Th 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 s 1. 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.

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 please help me to solve this based on the answers??!! Separable Differential Equations
number. The fraction of people who initially know the rumor is y(0) = yo, where 0sy, s1. Complete parts (a) to (c) below. Take the reciprocal of each side of the equation. 1-y C Solve for y. 1 y = kt. eC+1 Substitute 0 for t and yo for y to find C. (1-Yo C= In Yo (Simplify your answer.) Substitute C back into the found general solution. Textbook Print Sir P Pearson ENG DELL F2 F3 F4 F7 F5 F6 F8 F9 F10 F11 F12 PrtScr @ %23 & 2 6 8. E Y F C V M
Transcribed Image Text:number. The fraction of people who initially know the rumor is y(0) = yo, where 0sy, s1. Complete parts (a) to (c) below. Take the reciprocal of each side of the equation. 1-y C Solve for y. 1 y = kt. eC+1 Substitute 0 for t and yo for y to find C. (1-Yo C= In Yo (Simplify your answer.) Substitute C back into the found general solution. Textbook Print Sir P Pearson ENG DELL F2 F3 F4 F7 F5 F6 F8 F9 F10 F11 F12 PrtScr @ %23 & 2 6 8. E Y F C V M
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. Th 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. .... a. Solve this initial value problem and give the solution in terms of k and yo- Start by writing y'(1) = ky(1 – y) in separated form. 1. dy = kdt y(1-y) Integrate both sides. In 1-y = kt +C (Do not simplify.) Raise e to the power of each side of the equation. y = e kt.C 1-y Textbook Print Similar question P Pearson 1:14 PM ENG 11/13/2021 DELL F2 F3 F4 F5 F6 F7 F8 F9 F10 PriScr F11 F12 Insert Delete %23 %24 & 2 3 5 6. Backspace R Y U P D G J K B Alt Ciri Σ
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. Th 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. .... a. Solve this initial value problem and give the solution in terms of k and yo- Start by writing y'(1) = ky(1 – y) in separated form. 1. dy = kdt y(1-y) Integrate both sides. In 1-y = kt +C (Do not simplify.) Raise e to the power of each side of the equation. y = e kt.C 1-y Textbook Print Similar question P Pearson 1:14 PM ENG 11/13/2021 DELL F2 F3 F4 F5 F6 F7 F8 F9 F10 PriScr F11 F12 Insert Delete %23 %24 & 2 3 5 6. Backspace R Y U P D G J K B Alt Ciri Σ
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