Module 3  Logistic Growth  
Introduction  Lesson 1  Lesson 2  Lesson 3  SelfTest  
Lesson 3.3: Change in y  
In Lesson 3.2 you looked at the number of people infected each day and found an equation that fit the data. In this lesson you will use the TI89 to compute and graph the change in the number of infected people each day. That is, you will look at how the number of people infected is changing from one day to the next.
We have been using the number of infected people as the yvalues in our graph, so the change in the number of infected people will be named
y, which is read "delta y." The change in y is closely related to the concept of
Compute y If list1 and list2 can't be seen in the list editor, use the cursor movement keys to scroll to the left until they appear. You will store the values of y, the change in the number of infected people from one day to the next, in list3 by defining list3 as List(list2). Define List3 to be the Differences in List2
When the heading is highlighted you can enter a command for the entire list. Get the List( command
Get the variable "list2"
The changes in list2 are stored in list3. The first element in list3 is the difference between the second and first elements in list2. The second element in list3 is the difference between the third and second elements of list2. For this reason the values of y are also called differences. Create a Scatter Plot of the Differences
There is no eighth element in list 3 because there is no ninth element in list2 to use in computing a difference. In order to create a scatter plot of the differences, list 3 must have the same number of elements as list1 and list2. Make each list have the same number of elements.
The Plot type of Plot 2 should be "Scatter." Select the Mark Type To make the points for the differences different from the points for the number of people infected, let squares mark the points of the scatter plot of the differences.
Designate the Lists for x and for y
The daily differences, as shown with square points, form a bell shaped curve. 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 infected and that y recorded the number of new cases each day. The first significant relationship between the graph y and the graph y is that if y (the change in y) is positive, then y is increasing.
Secondly, the crest of the differences graph (the maximum value of
y) occurs at the same position where the logistic regression curve changes from
3.3.1 The values of y are always positive. What does this tell you about the original logistic scatter plot? Click here for the answer. 3.3.2 How is the peak of the difference graph related to the logistic curve? Click here for the answer. 

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