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Kendra Kilmer January 4, 2012
Section 1.2  Mathematical Models: A Catalog of Essential Functions
A
mathematical model
is a mathematical description (often by means of a function or an equation) of a realworld
phenomenon. The purpose of the model is to understand the phenomenon and perhaps to make predictions about
future behavior.
Defintion:
A
has the form
y
=
f
(
x
)=
mx
+
b
where
m
is the slope and
b
is the
y
intercept. For a linear function, the rate of change is constant, and thus the slope
can be interpreted as the rate of change of
y
with respect to
x
.
Example 1:
Sales of CDs have declined since 1999. Sales were $938
.
2 million in 1999 and $745
.
9 million in 2003.
a) Find a formula for sales,
S
, of CDs, in millions of dollars, as a linear function of the number of years,
t
, since
1999.
b) Interpret the slope.
c) Use the formula to predict CD sales in 2010.
Example 2:
Search and rescue teams work to find lost hikers. Members of the search team separate and walk
parallel to one another. The table shows the percent,
P
, of lost individuals found for various separation distances,
d
.
Separation distance d(ft)
20
40
60
80
100
Percent found, P
90
80
70
60
50
a) Explain how you know that
P
is a linear function.
b) What is the slope of the linear function? Give units and interpret.
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 Fall '08
 Allen
 Math, Derivative, Regression Analysis, Kendra Kilmer

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