Reasoning by Analogy/Models—Exercise
1.
Reasoning by analogy or models is a type of ______ argument that is ______.
A. inductive….certain
B. inductive…uncertain
C. deductive…certain
D. deductive…uncertain
2.
Complete the following analogy. blue : rainbow
A. colour : tulip
B. ball : soccer
C. drop : bucket
D. sunday : week
3.
A modern example of a weather model is based on the
A. farmers’ almanac
B. mental estimates of storm movements
C. numerical weather conditions and equations
D. observations of animal movements
4.
Sketch a visual model of the linear equation, 4x = 20.
5.
A Venn diagram is a visual model that can be used to illustrate logical relationships.
Circles (or other plane figures) represent sets of objects and the circles can be
separate, overlapping or within each other. What logical relationship is shown by
the following Venn diagram?
polygons
squares
6.
The exponential population growth model (sometimes called the Malthusian growth
model) is expressed as Nt = N0ert where N0 is the initial population, e is the base
of natural logarithms (2.71828…), r is the rate of increase of population, and t is
time.
(a) Why is this model useful?
(b) What is a significant limitation or pitfall of this model?
7.
A physical model can be used to discover or explain mathematical relations.
Analyze the model below and state the mathematical relation shown by the model.
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Answers
1. B
2. D
3. C
◘
◘ + ◘ + ◘ + ◘ = 20
4. using 1x =
5. All squares are polygons.
6. (a) You can predict a population at some time in the future without counting.
(b) Nothing can grow at a constant rate forever.
[or] The model is only useful for ideal conditions for a short initial period of time.
2
7. a – b2 = (a – b) (a + b)
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