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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.

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Presentation on theme: "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."— Presentation transcript:

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 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

2 a.Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).

3  2009 PBLPathways a.Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).

4  2009 PBLPathways a.Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).

5  2009 PBLPathways a.Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator).

6  2009 PBLPathways a.Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator). A percentage of pollutants removed can’t be negative or greater than 100.

7  2009 PBLPathways a.Use the restriction on p to determine the limitations on the horizontal-axis values (which are the x-values on a calculator). A percentage of pollutants removed can’t be negative or greater than 100.

8  2009 PBLPathways 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 ?

9  2009 PBLPathways 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 ? pC 00.00 10594.44 201337.50 302292.86 403566.67 505350.00 608025.00 7012483.33 8021400.00 9048150.00

10  2009 PBLPathways 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 ? pC 00.00 10594.44 201337.50 302292.86 403566.67 505350.00 608025.00 7012483.33 8021400.00 9048150.00

11  2009 PBLPathways 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 ? pC 00.00 10594.44 201337.50 302292.86 403566.67 505350.00 608025.00 7012483.33 8021400.00 9048150.00

12  2009 PBLPathways 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 ? pC 00.00 10594.44 201337.50 302292.86 403566.67 505350.00 608025.00 7012483.33 8021400.00 9048150.00

13  2009 PBLPathways 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 ? pC 00.00 10594.44 201337.50 302292.86 403566.67 505350.00 608025.00 7012483.33 8021400.00 9048150.00

14  2009 PBLPathways 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 ? pC 00.00 10594.44 201337.50 302292.86 403566.67 505350.00 608025.00 7012483.33 8021400.00 9048150.00

15  2009 PBLPathways c. Find the point on the graph that corresponds to p = 90. Explain the coordinates of this point. pC 00.00 10594.44 201337.50 302292.86 403566.67 505350.00 608025.00 7012483.33 8021400.00 9048150.00

16  2009 PBLPathways c. Find the point on the graph that corresponds to p = 90. Explain the coordinates of this point. pC 00.00 10594.44 201337.50 302292.86 403566.67 505350.00 608025.00 7012483.33 8021400.00 9048150.00

17  2009 PBLPathways 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.

18  2009 PBLPathways 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.

19  2009 PBLPathways 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.

20  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.

21  2009 PBLPathways 3.Enter the value 90 by pressing . 4.Press  to see the resulting y value, 48150.

22  2009 PBLPathways 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 .

23  2009 PBLPathways 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.

24  2009 PBLPathways 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.

25  2009 PBLPathways 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.

26  2009 PBLPathways 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.

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