Module 5  Logistic Growth  
Introduction  Lesson 1  Lesson 2  Lesson 3  Self Test  
Lesson 5.1: Simulating Logistic Growth with The SpreadofaRumor Experiment  
In this lesson the spread of a rumor will be simulated through an experiment that was conducted by a class of 25 students using the
The SpreadofaRumor Experiment The premise of the experiment is:
The total number of people who know the rumor is noted each day and recorded. On any given day some people who already know the rumor might be told again. These people will not be counted twice. The procedure to generate the data is described below. Numbering the Students and Setting the Calculators' Random Seed
Students in the experiment were numbered 1 through 25. Each student then entered their assigned number into their calculator's
Suppose a student's number was 19. That student entered 19 as the random seed, as follows:
Selection of the First Student The student who initially knew the rumor was selected by using the random integer command. That command can generate a random integer between 1 and 25.
In this experiment, the first student was selected by setting the calculator's random seed to 70 and generating a random number between 1 and 25.
Since 5 was the random integer generated, student 5 was selected as the first person to know the rumor. 5.1.1 Set your calculator's random seed to 100. Which student would be selected as the first student to know the rumor when you generate a random integer between 1 and 25? Click here for the answer. Generating the Experimental Data The initial student selected another person at random by entering the command randInt(1,25) on their calculator. Two people know the rumor at the end of the second day. Note: If the first person selected their own number, there would be only one person who knew the rumor on day two. On the third day, the people who knew the rumor each selected one more person at random by using the random integer command. The selected students may or may not have already been selected. If a student who had already been told was selected again, that person was not counted again. On subsequent days, each of the people who know the rumor selected another person at random. The Data Each day the total number of people who knew the rumor was recorded. This process continued until everyone had been told. The table below is a record of the total number of people that knew the rumor on each day. Everyone had been told the rumor by the eighth day.


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