Post on 17-Jan-2016
example 4 Cost-Benefit
Chapter 1.2
Suppose that the cost C of removing p% of the pollution from drinking water is givenby the model
5350 dollars
100
pC
p
a. Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).
b. Graph the function on the viewing window [0, 100] by [0, 50,000]. Why is it reasonable to graph this model on a viewing window with the limitation C > 0 ?
c. Find the point on the graph that corresponds to p = 90. Explain the coordinates of this point.
2009 PBLPathways
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5350 dollars
100
pC
p
a. Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).
2009 PBLPathways
5350 dollars
100
pC
p
a. Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).
2009 PBLPathways
5350 dollars
100
pC
p
a. Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).
100 0
100
p
p
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5350 dollars
100
pC
p
a. Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).
100 0
100
p
p
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5350 dollars
100
pC
p
a. Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).
100 0
100
p
p
A percentage of pollutants removed can’t be negative or greater than 100.
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5350 dollars
100
pC
p
a. Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).
100 0
100
p
p
A percentage of pollutants removed can’t be negative or greater than 100.
0 100p
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5350 dollars
100
pC
p
b. Graph the function on the viewing window [0, 100] by [0, 50,000]. Why is it reasonable to graph this model on a viewing window with the limitation C > 0 ?
2009 PBLPathways
5350 dollars
100
pC
p
b. Graph the function on the viewing window [0, 100] by [0, 50,000]. Why is it reasonable to graph this model on a viewing window with the limitation C > 0 ?
p C
0 0.00
10 594.44
20 1337.50
30 2292.86
40 3566.67
50 5350.00
60 8025.00
70 12483.33
80 21400.00
90 48150.00
2009 PBLPathways
5350 dollars
100
pC
p
b. Graph the function on the viewing window [0, 100] by [0, 50,000]. Why is it reasonable to graph this model on a viewing window with the limitation C > 0 ?
p C
0 0.00
10 594.44
20 1337.50
30 2292.86
40 3566.67
50 5350.00
60 8025.00
70 12483.33
80 21400.00
90 48150.00
5350 00 dollars
100 0C
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5350 dollars
100
pC
p
b. Graph the function on the viewing window [0, 100] by [0, 50,000]. Why is it reasonable to graph this model on a viewing window with the limitation C > 0 ?
p C
0 0.00
10 594.44
20 1337.50
30 2292.86
40 3566.67
50 5350.00
60 8025.00
70 12483.33
80 21400.00
90 48150.00
5350 10594.44 dollars
100 10C
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5350 dollars
100
pC
p
b. Graph the function on the viewing window [0, 100] by [0, 50,000]. Why is it reasonable to graph this model on a viewing window with the limitation C > 0 ?
p C
0 0.00
10 594.44
20 1337.50
30 2292.86
40 3566.67
50 5350.00
60 8025.00
70 12483.33
80 21400.00
90 48150.00
2009 PBLPathways
5350 dollars
100
pC
p
b. Graph the function on the viewing window [0, 100] by [0, 50,000]. Why is it reasonable to graph this model on a viewing window with the limitation C > 0 ?
p C
0 0.00
10 594.44
20 1337.50
30 2292.86
40 3566.67
50 5350.00
60 8025.00
70 12483.33
80 21400.00
90 48150.00
2009 PBLPathways
5350 dollars
100
pC
p
b. Graph the function on the viewing window [0, 100] by [0, 50,000]. Why is it reasonable to graph this model on a viewing window with the limitation C > 0 ?
p C
0 0.00
10 594.44
20 1337.50
30 2292.86
40 3566.67
50 5350.00
60 8025.00
70 12483.33
80 21400.00
90 48150.00
2009 PBLPathways
5350 dollars
100
pC
p
c. Find the point on the graph that corresponds to p = 90. Explain the coordinates of this point.
p C
0 0.00
10 594.44
20 1337.50
30 2292.86
40 3566.67
50 5350.00
60 8025.00
70 12483.33
80 21400.00
90 48150.00
2009 PBLPathways
5350 dollars
100
pC
p
c. Find the point on the graph that corresponds to p = 90. Explain the coordinates of this point.
p C
0 0.00
10 594.44
20 1337.50
30 2292.86
40 3566.67
50 5350.00
60 8025.00
70 12483.33
80 21400.00
90 48150.00
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Start by entering the equation.
1.Press the key to enter the function.
2.You’ll need to use x instead of p in the
expression. In the \Y1=, enter the
expression by pressing . Note
that the parentheses in the denominator
are essential.
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Now set the window.
3.Use the key to set the window.
4.Set Xmin = 0 and Xmax = 100.
5.Set Ymin= -5000 so that you can see
the bottom of the graph.
6.Set Ymax= 50000.
7.Set Xscl=10 and Yscl=5000.
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Finally, graph the equation.
7.Press the key to see the graph. Notice
that the tick marks are nicely spaced since
we picked Xscl=10 and Yscl=5000.
Using larger values would show fewer
tick marks because they would be more
widely spaced. Using smaller values
would show more tick marks since they
would be more closely spaced.
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Let’s find x = 90 on the graph using the .
1.To use , you’ll need to have the
function’s formula in the equation editor
like you see here. Graph the function by
pressing .
2.Press . You’ll see some x and y values
along the bottom of the screen.
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3. Enter the value 90 by pressing .
4. Press to see the resulting y value,
48150.
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You can also make a table to find x = 90.
1.To use the TABLE menu to find values
on the graph, the function’s formula
should already be entered in the equation
editor using .
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2. Press to access the TBLSET. Using
this screen, we’ll enable the calculator
so that you can supply an x-value and
the calculator will find the
corresponding y-value. You should
see a screen like the one to the right.
This indicates that the calculator will
create a table starting at x-values equal
to 0 at increments of 1 unit. Since
Indpnt and Depend are set to Auto,
the x-values and y-values will be
created automatically.
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3. To allow you to supply the x-value,
use your cursor control keys to move
to the Indpnt option and highlight
Ask and press . This allows you to
supply the independent variable value
or x-value.
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4. To see the table, press . You’ll see a
table of values like the one to the
right. Your x- and y-values may be
different.
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5. In the first column and first row, enter
x = 90 by pressing . The
corresponding y-value will appear in
the second column. The first row tells
us that to remove 90% of the
pollution, it will cost $48,150.You can
enter more x-values in the other rows
of the table as needed.