Intermath | Workshop Support

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?


Problem setup

I will need to set up Excel to help me see how many people will spread the rumor each day.  I can set up a formula where each day, the number grows exponentially, by powers of 2. 

 

Plans to Solve/Investigate the Problem

As I started to work on the Excel, and looked at the results, I noticed that each answer represented an exponent of 2. 

 

Investigation/Exploration of the Problem

1-May

2

2-May

4

3-May

8

4-May

16

5-May

32

6-May

64

7-May

128

8-May

256

9-May

512

10-May

1024

11-May

2048

12-May

4096

13-May

8192

14-May

16384

15-May

32768

16-May

65536

17-May

131072

18-May

262144

19-May

524288

20-May

1048576

21-May

2097152

22-May

4194304

23-May

8388608

24-May

16777216

 

 I can see that by Day 14, more than 8,000 people will have heard the rumor.  On Day 12, more than half the 8000 people will have heard the rumor (4096).  On the 8th day, exactly 256 people will have heard the rumor.  If the pattern continues until May 20th,  1,048,576 people will have heard the rumor.  To solve for “n” days, I would use the formula 2n (for example, on the 4th day , 24 people, or 2*2*2*2 or 16 people would have heard the rumor.

 

Extensions of the Problem

What would happen if 2 people each told 2 people per day?  How much quicker would the 8000 people be told?   What if 3 people each told 1 person per day?

Author & Contact
Meg  Ramsey
mramsey@rockdale.k12.ga.us

 

U Important Note: You should compose your write-up targeting an audience in mind rather than just the instructor for the course.

                                   You are creating a page to publish it on the web.

 

writeup.htm Failed! Click Here To Go Back!writeup_temp.htm Failed! Click Here To Go Back!