Question 698683: Burton High School has 1,500 students. During first period, a rumor is started when Susan tells three friends a secret. Each of Susan’s three friends tell three of their friends during second period, who in turn tell three different friends during third period. Assume each person tells the rumor to only three others.
Part 2
In an attempt to discredit the President, a member of the opposite political party wishes to start a scandalous rumor about him. He plans to tell people this rumor one week before election day and wants the entire population of the United States (that’s 250,000,000 people!) to know the rumor. He needs to figure out how many people he should tell (and they each will tell the same number of people) so that everyone will have heard the rumor by the seventh day.
Find the number of students who have heard the rumor at the end of the day. (Burton has 6 periods)
Find the number of people the evil politician need to tell so everyone in the United States will have heard the rumor by the seventh day. Remember; each person needs to tell the same number of people.
How do I solve this? Please help me! This is due the day after tomorrow and I need some serious help! Thank you soo much!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Burton High School has 1,500 students. During first period, a rumor is started when Susan tells three friends a secret. Each of Susan’s three friends tell three of their friends during second period, who in turn tell three different friends during third period. Assume each person tells the rumor to only three others.
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Find the number of students who have heard the rumor at the end of the day. (Burton has 6 periods)
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start of school day: 1 person
end of 1st period: 3
end of 2nd period: 3^2
end 3rd period: 3^3
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end of 6th period: 3^6 = 729
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Part 2
In an attempt to discredit the President, a member of the opposite political party wishes to start a scandalous rumor about him. He plans to tell people this rumor one week before election day and wants the entire population of the United States (that’s 250,000,000 people!) to know the rumor. He needs to figure out how many people he should tell (and they each will tell the same number of people) so that everyone will have heard the rumor by the seventh day.
Find the number of people the evil politician need to tell so everyone in the United States will have heard the rumor by the seventh day. Remember; each person needs to tell the same number of people.
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Let "x" be the number of people he needs to tell.
Solve: x^7 = 250,000,000
x = 250,000,000^(1/7)
x = 15.838
Round up to x = 16 persons.
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Cheers,
Stan H.
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