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Logistic Functions
Several years ago, we experienced one example of logistic growth: the COVID-19 pandemic.
This lesson will focus on logistic functions and their role in science, economics, medicine, etc.
The slide presentation outlines the steps used in analyzing and interpreting the data. Make sure you understand the role of the variables a, b, and c.
Desmos is making our lives easier by including a list of regressions. Using the instructions for problem 2, generate the logistic graph and the function.
Don't rush through this presentation - use Desmos to work through the problem as you view the presentation.
Problem Example 2
Jack and Diane live in a small town of 50 people.
Unfortunately, both Jack and Diane have a cold.
Those who come in contact with someone who has this cold will catch a cold.
Image 1: To generate a regression function and graph, click on the icon located in the upper left of the data table.
Image 2: After clicking on the icon, a regression menu will appear. Click on the drop-down menu to access Logistic Regression.
The following data represents the number of people in the small town who have caught a cold after t days.
A. Using Desmos, plot the data.
B. Set x intervals -1 < x1 < 10
Set y intervals 0 < y1 < 50
C. Using Images 1 and 2, generate the Logistic graph and function.
D. Identify the values for a, b, and c.
E. Using the model, answer the following:
i. What is the maximum number of people who will catch a cold?
ii. How long will it take for 46 people to catch a cold?
iii. Identify the rate at which the cold was spreading.
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