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Air Pollution Reduction - Cost-Benefit Analysis Coal has long been a reliable source of American energy, but it comes with tremendous costs because it is very dirty. When coal is burned, it releases a number of airborne toxins and pollutants, including mercury, lead, sulfur dioxide, nitrogen oxides, particulates, and various other heavy metals which can have harmful environmental impacts in addition to CO2. The function below relates the cost C (in $1000) to remove x percent of the air pollutants for a hypothetical power company which burns coal to generate electricity. A function such as this is called a cost-benefit function because it relates a cost (the price of implementing practices to remove the pollution) and a benefit (the removal of the air pollutants from the energy-generating process). C(x) = 540x / (100-x) for 0 ≤ x < 100 Use the above function to show that the cost of removing 40% of the air pollutants would be $360,000. Then compute the cost (in dollars) for the company to remove 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, and 95% of the air pollutants. Organize your results in a table and make a scatterplot of the points using Desmos. What trend do you observe? What would be the increased cost (in dollars) for the company if they were to add processes that would increase the amount of pollutants removed from 50% to 60%, from 60% to 70%, from 70% to 80%, and from 80% to 90%? Comment on any trend that may be noticed. According to the cost-benefit function, would it be possible for the company to remove 100% of the air pollutants? Explain why this does or does not make sense. The domain of C(x) is restricted to 0 ≤ x < 100. Explain why this makes sense in the context of this model. If the company decides they can reasonably budget $2 million for pollution control, what percentage of air pollutants can be removed (to the nearest tenth of a percent)? Sketch the graph of C(x) (for 0 ≤ x < 100) using Desmos. What is the range of C(x)? Explain why the range makes sense in the context of the problem.

Name: air pollution reduction cost benefit analysis coal has long been a reliable source of american energy but it comes with tremendous costs because it is very dirty when coal is burned it relea 07013
Uploaded: 2022-12-21T17:44:43-08:00
Duration: 10 min 13 s
Channel: Bcrypt_Sha256$$2B$12$Koudzt7Vugfesdqzt.Btsohdsno3/5Wc5Bsgjhyqjgxswzij15Z06 Bcrypt_Sha256$$2B$12$Koudzt7Vugfesdqzt.Btsoec1F7Nikxndin/Owbntbjji9Jzcznki
Description: air pollution reduction cost benefit analysis coal has long been a reliable source of american energy but it comes with tremendous costs because it is very dirty when coal is burned it relea 07013

          Air Pollution Reduction - Cost-Benefit Analysis
Coal has long been a reliable source of American energy, but it comes with tremendous costs because it is very dirty. When coal is burned, it releases a number of airborne toxins and pollutants, including mercury, lead, sulfur dioxide, nitrogen oxides, particulates, and various other heavy metals which can have harmful environmental impacts in addition to CO2.
The function below relates the cost C (in $1000) to remove x percent of the air pollutants for a hypothetical power company which burns coal to generate electricity. A function such as this is called a cost-benefit function because it relates a cost (the price of implementing practices to remove the pollution) and a benefit (the removal of the air pollutants from the energy-generating process).
C(x) = 540x / (100-x)
for 0 ≤ x < 100
Use the above function to show that the cost of removing 40% of the air pollutants would be $360,000. Then compute the cost (in dollars) for the company to remove 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, and 95% of the air pollutants. Organize your results in a table and make a scatterplot of the points using Desmos. What trend do you observe?
What would be the increased cost (in dollars) for the company if they were to add processes that would increase the amount of pollutants removed from 50% to 60%, from 60% to 70%, from 70% to 80%, and from 80% to 90%? Comment on any trend that may be noticed.
According to the cost-benefit function, would it be possible for the company to remove 100% of the air pollutants? Explain why this does or does not make sense.
The domain of C(x) is restricted to 0 ≤ x < 100. Explain why this makes sense in the context of this model.
If the company decides they can reasonably budget $2 million for pollution control, what percentage of air pollutants can be removed (to the nearest tenth of a percent)?
Sketch the graph of C(x) (for 0 ≤ x < 100) using Desmos. What is the range of C(x)? Explain why the range makes sense in the context of the problem.

Added by Tina L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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12/21/2022

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Given the function C(x) = 540x(100-x), where x is the percentage of air pollutants removed, we substitute x with 40 to find the cost for 40% removal. \[ C(40) = 540 \times 40 \times (100 - 40) \] \[ C(40) = 540 \times 40 \times 60 \] \[ C(40) = 540 \times 2400 Show more…

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Air Pollution Reduction - Cost-Benefit Analysis Coal has long been a reliable source of American energy, but it comes with tremendous costs because it is very dirty. When coal is burned, it releases a number of airborne toxins and pollutants, including mercury, lead, sulfur dioxide, nitrogen oxides, particulates, and various other heavy metals which can have harmful environmental impacts in addition to CO2. The function below relates the cost C (in $1000) to remove x percent of the air pollutants for a hypothetical power company which burns coal to generate electricity. A function such as this is called a cost-benefit function because it relates a cost (the price of implementing practices to remove the pollution) and a benefit (the removal of the air pollutants from the energy-generating process). C(x) = 540x / (100-x) for 0 ≤ x < 100 Use the above function to show that the cost of removing 40% of the air pollutants would be $360,000. Then compute the cost (in dollars) for the company to remove 50%, 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%, and 95% of the air pollutants. Organize your results in a table and make a scatterplot of the points using Desmos. What trend do you observe? What would be the increased cost (in dollars) for the company if they were to add processes that would increase the amount of pollutants removed from 50% to 60%, from 60% to 70%, from 70% to 80%, and from 80% to 90%? Comment on any trend that may be noticed. According to the cost-benefit function, would it be possible for the company to remove 100% of the air pollutants? Explain why this does or does not make sense. The domain of C(x) is restricted to 0 ≤ x < 100. Explain why this makes sense in the context of this model. If the company decides they can reasonably budget $2 million for pollution control, what percentage of air pollutants can be removed (to the nearest tenth of a percent)? Sketch the graph of C(x) (for 0 ≤ x < 100) using Desmos. What is the range of C(x)? Explain why the range makes sense in the context of the problem.

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00:01 The function c of x equals 540x over 100 minus x, where x is greater than or equal to zero and less than 100, relates the cost to c in thousands of dollars to remove x percent of air pollutants for a company that burns coal to generate electricity.

00:14 First, we want to show that the cost of removing 40 percent of pollutants would be 360 ,000, and we're going to compute the cost in dollars to remove 50, 55, 60, 65, 70, 75, 80, 85, 80, 85, and 90, and 95 percent of pollutants.

00:29 Make a table of these results and make a scatter plot of the points.

00:33 So first, let's show that the cost of removing 40 % gives $36 ,000.

00:38 So that means we would just figure out c of 40.

00:41 We would let x be 40, since that represents the percent.

00:45 So that would just be 540 times 40 over 100 minus 40.

00:51 And if we do 540 times 40, 540 times 40, that gives 21.

01:00 Thousand six hundred divided by one hundred minus forty is sixty so if we do 21 ,600 divided by sixty that gives us three hundred and six and since it told us that the cost was in thousands of dollars we would just multiply that by a thousand so that would give us thirty six thousand dollars okay next we want to make this table showing the cost to make all these percentages here.

01:35 So we'll let this be x and this is the cost.

01:40 So we need to plug in 50, 55, 60, 65, 70, 75, 80, 80, 85, 80, 85, and 95.

01:53 And we need to keep in mind that this cost is in thousands of dollars, and thousands of dollars so if we plug in 50 we actually get 540 if we plug in 55 we would get 660 if we plug in 60 we get 810 65 gives us 1 ,0 .9 70 gives us 1 ,260 75 gives us 1 ,620 80 gives us 20, 80 gives us 20 or 2 ,160, 85 gives us 3 ,060, 90 gives us 4 ,860, and 95 gives us 10 ,260.

02:41 So let's plot all these points in a scatter plot, and we're going to use desmos .com to do that.

02:49 So i'm just going to plug all those points in here.

02:51 So i've got this zoomed out and those points plugged in.

02:54 I've got my x window go from like 0 to 110, and then my y's go.

03:01 From like zero to about a little over 10 ,000 there.

03:05 So we can see all those data points now.

03:10 And we can see that it's definitely increasing.

03:12 Look like it's the further we go, the more increases between each percent increase.

03:18 So this is getting steeper and steeper, definitely increasing.

03:21 Okay, the next part we want to do is we want to find the increased cost in dollar for the company to increase the amount of pollutants removed from 50 to 60 percent.

03:31 So they were just to move from 50 to 60%.

03:39 That would increase the cost from 540 to 8 .10.

03:43 So that increase in cost would just be 8 .10 minus 540.

03:47 And remember, those are in thousands.

03:49 So if we just do 810 minus 540, that would give us 270.

03:53 So 270k ,000.

03:58 And then to go from 60 to 70, to go from 60 to 70, that's 1260 minus 810.

04:08 If we do that, that's a $450 ,000 increase.

04:15 If we go from 70 to 80, that's 1 ,260 to 2160.

04:22 So that would be 2 ,160 minus 1 ,260.

04:30 And that gives about 900 ,000.

04:37 And then to go from 80 to 90%, that's going from 4860 minus 2 ,160.

04:47 And that would give us 27 ,000.

04:53 Thousand so we can see that these increases actually increase for the first increase we just went up 270 ,000 then we went up 450 ,000 so that actually is why the graph gets steeper those increases are getting further apart those points from one each since we're going up by 10 % we can see we're going up more and more each time it's not a constant increase.

05:25 Okay, according to the function c of x, is it possible to remove 100 % of the air pollutants? so that function c of x was 540x over 100 minus x...

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