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The Rumors Problem
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:
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
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.
- Describe the shape of the new graph in terms of the x and y axes.
(Hint: How is it different from the first graph?)
- 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?
- What else is spread in the real world, similar to the way that
rumors are spread?
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?