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While on an unauthorised trip to the local fast food restaurant during their study period, a pair of Year 12 students are convinced that they have just seen the Prime Minister buying a hamburger. On returning to the school, dp =1 p(1- p), where p is the their amazing discovery spreads throughout the school community at the rate proportion of the school community that has already heard the rumour, t minutes after their return to school. (a) What proportion of the school community has heard the rumour when it is spreading most rapidly? By the beginning of the afternoon period, 20% of the school community had already heard the rumour. (b) Find p(t), at time t minutes since the beginning of the afternoon period, given 10 1 1 1 %3D p(1-p) p p-1' (c) At what time (correct to the nearest minute) is the rumour spreading most rapidly?

While on an unauthorised trip to the local fast food restaurant during their study period, a pair of Year 12 students are convinced that they have just seen the Prime Minister buying a hamburger. On returning to the school, dp =1 p(1- p), where p is the their amazing discovery spreads throughout the school community at the rate proportion of the school community that has already heard the rumour, t minutes after their return to school. (a) What proportion of the school community has heard the rumour when it is spreading most rapidly? By the beginning of the afternoon period, 20% of the school community had already heard the rumour. (b) Find p(t), at time t minutes since the beginning of the afternoon period, given 10 1 1 1 %3D p(1-p) p p-1' (c) At what time (correct to the nearest minute) is the rumour spreading most rapidly?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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31 While on an unauthorised trip to the local fast food restaurant during their study period, a pair of Year 12 students are convinced that they have just seen the Prime Minister buying a hamburger. On returning to the school, dp - their amazing discovery spreads throughout the school community at the rate 1O P(1-p), where p is the proportion of the school community that has already heard the rumour, t minutes after their return to school. (a) What proportion of the school community has heard the rumour when it is spreading most rapidly? By the beginning of the afternoon period, 20% of the school community had already heard the rumour. dt 1 1 (b) Find p(t), at time t minutes since the beginning of the afternoon period, given p(1– p) p p-1' (c) At what time (correct to the nearest minute) is the rumour spreading most rapidly?
Transcribed Image Text:31 While on an unauthorised trip to the local fast food restaurant during their study period, a pair of Year 12 students are convinced that they have just seen the Prime Minister buying a hamburger. On returning to the school, dp - their amazing discovery spreads throughout the school community at the rate 1O P(1-p), where p is the proportion of the school community that has already heard the rumour, t minutes after their return to school. (a) What proportion of the school community has heard the rumour when it is spreading most rapidly? By the beginning of the afternoon period, 20% of the school community had already heard the rumour. dt 1 1 (b) Find p(t), at time t minutes since the beginning of the afternoon period, given p(1– p) p p-1' (c) At what time (correct to the nearest minute) is the rumour spreading most rapidly?
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