Question 782139: Tara is 7th grader student at Swat Middle School in Bugsville, USA. She decides to start a rumor that the town of Bugsville is going to declare March 12 as National Bug Day and all schools will be closed for the day. On the first day Tara tells two students the rumor with the instructions that each of these students repeats the rumor to two more students the second day. Each of these new students is to repeat the rumor to two more students on the third day, and so on. For example, on the first day two students know the rumor; on the second day four more students will know the rumor; on the third day eight more students will know the rumor, and so on. How many new students will be told the rumor on day 12? If Tara starts her rumor on May 15th and there are 8000 students in the school district, will all of the town's students hear the rumor before May 30th?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Tara is 7th grader student at Swat Middle School in Bugsville, USA. She decides to start a rumor that the town of Bugsville is going to declare March 12 as National Bug Day and all schools will be closed for the day. On the first day Tara tells two students the rumor with the instructions that each of these students repeats the rumor to two more students the second day. Each of these new students is to repeat the rumor to two more students on the third day, and so on. For example, on the first day two students know the rumor; on the second day four more students will know the rumor; on the third day eight more students will know the rumor, and so on.
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How many new students will be told the rumor on day 12?
2^0+2+2^2+2^3+2^4+...+2^11 = 1[(2^12 - 1)/(2-1)] = 4095
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If Tara starts her rumor on May 15th and there are 8000 students in the school district, will all of the town's students hear the rumor before May 30th?
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Sum = 1[(2^16 - 1)/(2-1)] = 65535
Ans: yes
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Cheers,
Stan H.
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