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?
Decide how much the number of people
who know the rumor will increase as each day goes by until at least 8000 people
have heard the rumor. Can this happen before the 20th day? Each day
each person who knows the rumor will tell two more. On what day will about
4000 people know the rumor? What is the formula for determining the number
of people who know the rumor on a given day?
Plans to Solve/Investigate the
I will start by making a diagram to
show the first person telling 2 more, those 2 each telling 2 more, and so on.
Put the date beside each progression, beginning with May 1. The diagram
quickly becomes a pattern where each amount is doubling day by day.
Investigation/Exploration of the
May 1 = 1
May 2 = 2
May 3 = 4
May 4 = 8
May 5 = 16 until May 14 = 9,192, over
the 8,000 person mark by the deadline of May 14.
May 13 = 4096, over the 4,000 mark
(the 13th day).
256 people will have heard the rumor
by May 9, day 9.
By May 20 588,288 people will have
heard the rumor.
The pattern here is the amount of
people on a certain day equals 2 times 2 to the (day - 1) power. For
example, day 20 = 2 * 2 to the 19th power. The number of new people would
be the number of people on the (nth -1) day * 2.
Extensions of the Problem
Outside of math, use this to
emphasize character ed - not to spread rumors about each other!