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Q
uantitative
R
easoning &
P
roblem
S
olving
418
© 2014 Pacific Crest
D
iscovery
Finding out for yourself
Construct a mathematical model to estimate the total cost of owning and operating a vehicle of your
choice. The only output variable should be the total cost in dollars. Initially, use the number of miles
driven as the only input variable. Construct a graph of your models input and output for class. Keep
refining your model to account for every cost you can imagine.
W
hat Do You Already Know?
Tapping into your existing knowledge
1. When have you determined the answer to a problem like this without a model? What did you do to
find the answer then?
2. What is the process for expressing this relationship mathematically?
3. When refining your model how do you incorporate new input variables?
4. How do you know when to stop refining your model?
M
athematical Language
Terms and notation
algorithm
—
a set of steps that are followed in order to solve a mathematical problem or to complete
a computer process
refinement
—
a model that has been altered to solve the problem with more accuracy or efficiency
abstract
—
to extract the most important parts of a situation or phenomenon
embed
—
to incorporate into a different environment
mechanism
— a process or system that is used to produce a particular result
I
nformation
What you need to know
R
esources
M
ethodology
C
onstructing a
M
athematical
M
odel
Scenario:
Construct a mathematical model for estimating the volume of a car tire.
Step
Explanation
Watch it Work!
1.
What is your
purpose?
Identify the situation or scenario that you
want to study.
What is the volume of a tire?
2.
Gain
background
knowledge
Research the field or area in which this
situation occurs.
A car tire has the following shape