Technology for Chapter 2: The Modeling Process ...
Technology for Chapter 2: The Modeling Process, Proportionality, and Geometric Similarity.
In chapter 2, we estimate the slope of proportionality line using the two point method. Given (x1,y1) and (x2,y2) then the slope, k, is
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We will use the following to illustrate the use of technology.
Proportionality/Geometric Similarity Modeling
1. PURPOSE: To provide the student the opportunity to develop proportionality arguments and test them using technology.
2. OBJECTIVE: Determine if the hearts of mammals are geometrically similar using your knowledge of proportionality models and technology. Provide a summary of your analysis using the following data to support or refute your argument.
Heart Weight Length of cavity of
Animal (in grams) left ventricle (in)
Mouse 0.13 0.55
Rat 0.64 1.00
Rabbit 5.80 2.20
Dog 102.00 4.00
Sheep 210.00 6.50
Ox 2030.00 12.00
Horse 3900.00 16.00
3. PROCEDURE:
a. Develop the proportionality model relating heart weight (HW) to the length (L) of the cavity of the left ventricle. You should get HW ( L3.
b. Test the proportionality model using the data provided. Testing a proportionality model often involves the following steps:
(1) Enter the raw observed data into your calculator and computer.
(2) Plot the raw data to check for smoothness and potential "outliers", and to give you a "feel" of the type of proportionality you might find.
(3) Make any necessary transformations to the data for the model.
(4) Plot the transformed data to test the proportionality (It must form a straight line through the origin).
(5) Estimate the constant of proportionality (eyeball a straight line through the origin and use slope =rise/run to find the constant).
(6) Obtain an overlay of the actual vs. computed data or find the errors (yactual-ypredicted) to see if your model properly captures the trend of the data. Comment about the fit.
Proportionality Template
Enter the raw data as Xdata and Ydata
Enter the transformation to X or Y as needed
Give the point to use in the slope
Interpret the output.
We illustrate with the same lab.
Heart Weight Length of cavity of
Animal (in grams) left ventricle (in)
Mouse 0.13 0.55
Rat 0.64 1.00
Rabbit 5.80 2.20
Dog 102.00 4.00
Sheep 210.00 6.50
Ox 2030.00 12.00
Horse 3900.00 16.00
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