Math Forum - Problem of the Week


Rumors

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The Rumors Problem

Introduction

Shanika has learned from a phone call that William has dyed his hair green. She can't wait to share this rumor with all the people at school. She stands at the door to the cafeteria, where people are entering every ten seconds, and tells every person who enters.



In real life, Shanika would probably not stand at the door of the cafeteria and tell the rumor to everyone who walks in. Here is a more realistic scenario:

Simulation

Shanika has just learned that William has dyed his hair green. Shanika is very excited and runs around telling the rumor to everybody she meets. She makes a point of telling people not to tell anyone else.

What will the shape of the graph be?

Will it be
1.   2.   3.  


To find the shape of the new graph, please click on the link below to show the applet window and run the simulation. Use what you learn from the simulation to answer the questions.

Click To Show Applet Window

Questions:

  1. Describe the shape of the new graph in terms of the x and y axes. (Hint: How is it different from the first graph?)

  2. What happened differently in how Shanika spread the rumor at the cafeteria door from how she spread it by running around during lunch that changed the way the graph looked?

  3. What else is spread in the real world, similar to the way that rumors are spread?
Bonus:

What if each person Shanika tells just can't keep the promise not to tell anyone else, and tells the rumor to other people? How will this change the shape of the graph?

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