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 transcript:

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

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 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 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 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 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.

 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.

 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 ?

 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

 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

 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

 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

 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

 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

 2009 PBLPathways c. Find the point on the graph that corresponds to p = 90. Explain the coordinates of this point. pC

 2009 PBLPathways c. Find the point on the graph that corresponds to p = 90. Explain the coordinates of this point. pC

 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.

 2009 PBLPathways Now set the window. 3.Use the  key to set the window. 4.Set Xmin = 0 and Xmax = Set Ymin= so that you can see the bottom of the graph. 6.Set Ymax= Set Xscl=10 and Yscl=5000.

 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.

 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.

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

 2009 PBLPathways You can also make a table to find x = To use the TABLE menu to find values on the graph, the function’s formula should already be entered in the equation editor using .

 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.

 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.

 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.

 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.