Homework Help is Here – Start Your Trial Now!
Math
Calculus
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, s 1. Complete parts (a) to (c) below. ..... y 1-y Take the reciprocal of each side of the equation. 1-y y Solve for y. %3= -kt. C+1 Substitute 0 for t and yo for y to find C. C= (Simplify your answer.) %3D Textbook Print Clear all Check answer THIS COurse (MATH ZZT0STUD rat ZUZTS Das TRES/COCIrancaicuUs tariy Taiscenaeritais, se ENG

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, s 1. Complete parts (a) to (c) below. ..... y 1-y Take the reciprocal of each side of the equation. 1-y y Solve for y. %3= -kt. C+1 Substitute 0 for t and yo for y to find C. C= (Simplify your answer.) %3D Textbook Print Clear all Check answer THIS COurse (MATH ZZT0STUD rat ZUZTS Das TRES/COCIrancaicuUs tariy Taiscenaeritais, se ENG

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
See similar textbooks
icon
Related questions
Question
Can someone please explain it to me ASAP??!! The part starts 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. 1-y Take the reciprocal of each side of the equation. 1-y - kt.C Solve for y. y = e- kt. eC+1 Substitute 0 for t and y, for y to find C. C= (Simplify your answer.) Textbook Print Clear all Check answer ENG ? O DELL E R F G H K 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. 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. 1-y Take the reciprocal of each side of the equation. 1-y - kt.C Solve for y. y = e- kt. eC+1 Substitute 0 for t and y, for y to find C. C= (Simplify your answer.) Textbook Print Clear all Check answer ENG ? O DELL E R F G H K Σ
ts 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. a. Solve this initial value problem and give the solution in terms of k and yo we eBook Start by writing y' (t) = ky(1-y) in separated form. ook Contents Y(1-y) dy = kdt ar Success Integrate both sides. y In = kt +C (Do not simplify.) 1-y nedia Library 1-v ase Options Raise e to the power of each side of the equation. y 1-y ssible Resourc kt ussions Take the recinrocal of each side of the equation rse Tools Textbook Print Clear all Check answer TIS Course tiVAT ZUZT ntais, se ENG 会の DELL F4 FS F9 F12 Delete %23 # 2$ & * 2 3 4 5 6 8 Backsp E R A S D G K L V B Alt Alt Ctri <-Home Σ (7 N
Transcribed Image Text:ts 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. a. Solve this initial value problem and give the solution in terms of k and yo we eBook Start by writing y' (t) = ky(1-y) in separated form. ook Contents Y(1-y) dy = kdt ar Success Integrate both sides. y In = kt +C (Do not simplify.) 1-y nedia Library 1-v ase Options Raise e to the power of each side of the equation. y 1-y ssible Resourc kt ussions Take the recinrocal of each side of the equation rse Tools Textbook Print Clear all Check answer TIS Course tiVAT ZUZT ntais, se ENG 会の DELL F4 FS F9 F12 Delete %23 # 2$ & * 2 3 4 5 6 8 Backsp E R A S D G K L V B Alt Alt Ctri <-Home Σ (7 N
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer