Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from...
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Transcript of Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from...
![Page 1: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/1.jpg)
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
![Page 2: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/2.jpg)
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).
![Page 3: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/3.jpg)
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).
![Page 4: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/4.jpg)
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
![Page 5: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/5.jpg)
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
![Page 6: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/6.jpg)
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
A percentage of pollutants removed can’t be negative or greater than 100.
![Page 7: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/7.jpg)
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
A percentage of pollutants removed can’t be negative or greater than 100.
0 100p
![Page 8: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/8.jpg)
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 ?
![Page 9: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/9.jpg)
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
![Page 10: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/10.jpg)
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
![Page 11: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/11.jpg)
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 10594.44 dollars
100 10C
![Page 12: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/12.jpg)
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
![Page 13: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/13.jpg)
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
![Page 14: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/14.jpg)
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
![Page 15: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/15.jpg)
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
![Page 16: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/16.jpg)
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
![Page 17: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/17.jpg)
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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.
![Page 18: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/18.jpg)
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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.
![Page 19: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/19.jpg)
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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.
![Page 20: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/20.jpg)
2009 PBLPathways
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.
![Page 21: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/21.jpg)
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3. Enter the value 90 by pressing .
4. Press to see the resulting y value,
48150.
![Page 22: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/22.jpg)
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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 .
![Page 23: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/23.jpg)
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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.
![Page 24: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/24.jpg)
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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.
![Page 25: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/25.jpg)
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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.
![Page 26: Example 4 Cost-Benefit Chapter 1.2 Suppose that the cost C of removing p% of the pollution from drinking water is given by the model a.Use the restriction.](https://reader036.fdocuments.us/reader036/viewer/2022062804/5697bf8c1a28abf838c8bfc9/html5/thumbnails/26.jpg)
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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.