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Write-up


Title

Spreading Rumors 

Problem Statement

A rumor starts by someone telling the rumor to two people on May 1. Each of those two people are responsible for telling the rumor to two others on the next day (May 2).At this time seven people know the rumor. On May 3, the four people who heard the rumor on May 2 must each tell two more people. It is important for 8000 people to hear the rumor by May 14. Is this outcome likely to occur if the pattern for spreading the rumor continues as started?

On what day will approximately one-half of the 8000 have heard the rumor? On what day will 256 new people be told the rumor? If the rumor process continues until May 20,how many new people will hear the rumor on that day?

If the rumor process continues for n days, how many new people will be told the rumor on the nth day? What will be the total number of people who know the rumor on that day?.


 

Plans to Solve/Investigate the Problem

I plan to set up a function table to look for a pattern.

 

Investigation/Exploration of the Problem

I created a function table.

0

1

2

3

4

1

3

7

15

31

 I noticed that each column increases by powers of 2.  3-1=2, 7-3=4, 15-7 = 8, 31-15 = 8. I then created a spreadsheet to find the answers to the questions.

0

1

1

3

2

7

3

15

4

31

5

63

6

127

7

255

8

511

9

1023

10

2047

11

4095

12

8191

13

16383

14

32767

15

65535

16

131071

17

262143

18

524287

19

1048575

20

2097151

 

Eight thousand people will know by the 12th day.

On the 8th day 256 new people were told the rumor.

 

Formula: number of people who know on the nth day = number of people who knew on the n-1 day + 2^nth day.

Author & Contact

Dottie Mitcham


 

 

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