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 Write-up

Title

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

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