Module 5  Logistic Growth  
Introduction  Lesson 1  Lesson 2  Lesson 3  SelfTest  
Lesson 5.3: Change in y  
In Lesson 5.2 you looked at the number of people who know a rumor each day and found an equation that fit the data. In this lesson you will use the TI83 to compute and graph the change in the number of people who know the rumor each day.
We have been using the number of people who know a rumor as the yvalues in our graph. The change in the number of people who know the rumor each day will be named
y, which is read "delta y." The change in y,
y, is closely related to the concept of a
On a given day, the change in the total number of people who know the rumor is equal to the number of new people who were told on that day. y and the List Command List is a command on the TI83 that computes the differences between subsequent values of a list. It can generate the number of new people told each day, y. The TI83 can be instructed to automatically store the values of y into L3 by using List. Define L3 to be the Differences in L2
When the heading is highlighted you can enter a command for the entire list. Entering The List( Command
The differences in subsequent values of L2 are stored in L3.
For this reason the values of y are also called differences. Create a Scatter Plot of the Differences There is no eighth element in L3 because there is no ninth element in L2 to use in computing an eighth difference. In order to create a scatter plot of the differences, L3 must have the same number of elements as L1 and L2. The eighth number of L3 can be any number but it is usually better for the number to fit the pattern of values in L3.
Make Each List Have the Same Number of Elements.
Graph the Scatter Plot of the Differences
The daily differences, as shown with "plus" symbols, form a bellshaped curve. The first three data points for the scatter plot of the differences can not be seen in this graph, but you can find them by Tracing Plot2. The Relationship Between y and y There are two significant relationships between the graph of y and the graph of y. Recall that y accumulated the total number of people who know the rumor and that y recorded the number of new people told each day.
Both the maximum value of y and the point of inflection on the graph of y occur on Day 5, the day that has the highest number of new people who know the rumor and the day where the increase in subsequent values of y begins to slow. 5.3.1 The values of y are always positive in a logistic model. What does this tell you about the original logistic scatter plot? Click here for the answer. 5.3.2 How is the peak of the difference graph related to the logistic curve? Click here for the answer. 

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