Math 150, Fall 2007,
c Benjamin Aurispa
Chapter 2, Continued
2.6 Modeling with Functions
This section is very similar to 1.6, except now we are using functions. When modeling functions,
1. Choose the variable. Sometimes the problem will tell you what to let your variable be.
2. Write all other unknowns in terms of your chosen variable.
3. Set up the model by writing the function in terms of the variable.
4. Interpret and use the model to answer questions.
Examples
1. The height of a cylinder is 3 times its radius. Find a function that models the volume
V
of the cylinder
in terms of its radius,
r
.
2. A box with a square base is to have a volume of 12 ft
3
. Find a function that models the surface area
S
of the box in terms of the length
x
of one side of its base.
3. Suppose I have 20 ft of wood to fence in a rectangular pen.
(a) Find a function that models the area of the pen as a function of the width of the pen.
(b) Find the dimensions of the largest area I can fence. What is the largest area?
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Math 150, Fall 2007,
c Benjamin Aurispa
4. Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
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 Fall '08
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 Math, $5, Inverse function, 20 ft, Injective function, Benjamin Aurispa

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