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

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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 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.