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Modeling Logistic Functions using a Graphing Calculator
Follow these steps to generate a data table, plot the data points, and generate the logistic model for the data.
Practice Problem
You planted a sunflower seedling and kept track of its height(h) in centimeters over time(t) in weeks.
Find a model that gives h as a function of t.
Press the STAT button.
Select 1: Edit
Include under L1: {0, 1, 2, 3, 4, 5, 6, 7, 8}
Include under L2: {18, 33, 56, 90, 130, 170, 203, 225, 239}
Press 2nd Y= (STATPLOT)
Select 1; Select: On; Select Type: Scattered; Select square or + sign.
Press ZOOM button
Select 9: ZoomStat
A scattered graph should be graphed.
We now want to determine the logistic function.
Remember the general form for a logistic function is: Formula (Right --->
The value of c is the upper limit of the size of y, and y = c is a horizontal asymptote of the curve.
Press the CLEAR button.
Press STAT button and move the cursor to CALC.
Move the cursor to B: Logistic, then press ENTER.
The word Logistic with a flashing cursor should appear.
Press the ENTER button.
It will take some time for the calculator to generate the values for a, b, and c.
The general form of the logistic equation should appear on your screen.
a = 13.06939386
b = 0.65088999
c = 256.055474
We want to graph this information. We have a simple way to place it in the Y = without having to type the values for a, b, and c.
Press the Y = button.
Press the VARS button.
Move the cursor down to 5: Statistics (or press 5).
Move the cursor to EQ.
Press 1: RegEQ.
Press the Y = button.
Press the GRAPH button.
The logistic equation should fit the scattered points.
Exercise 1
During the winter of 2020, the world experienced a spread of a very contagious disease, the Coronavirus.
We know that a person can pass the disease to another through mere proximity.
Let's assume you and your 29 classmates are in the room and no one leaves or enters.
Bottom row: Number of people infected.
~ Draw a scatter plot of the data
~ Find a model that gives y as a function of t using the logistic regression feature of a graphing calculator.
~ Graph the logistic regression function over the scatter plot of the data.
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