SOLUTION: Burton High has 1500 Students. During 1st period, a rumor is started when susan tells a secret. each of susans three friends tell three of thier friends during second period , who

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Burton High has 1500 Students. During 1st period, a rumor is started when susan tells a secret. each of susans three friends tell three of thier friends during second period , who       Log On

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Question 1960: Burton High has 1500 Students. During 1st period, a rumor is started when susan tells a secret. each of susans three friends tell three of thier friends during second period , who in turn tell three different friends during third period. assume each person tells the rumor to only three others.
find the number of students who have heard the rumor at the end of the day.( burtin has 6 periods)
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
ignoring the first person for now, lets look at the end of the periods...
at end of first period = 3 new people told
at end of second period = 3x3 new people told
at end of third period = 3x3x3 new people told
at end of fourth period = 3x3x3x3
at end of fifth period = 3x3x3x3x3
at end of sixth period = 3x3x3x3x3x3
so a=3, ratio = 3, n = 6
Sn = a(r^n-1)/(r-1) so S=3(3^6-1)/(3-1)
S = 3x(729-1)/2
S=1092 plus the original person = 1093 people by the end of the day.