Project: Waste Generation and Disposal

Waste Generation and Disposal

Introduction

You are working for the Environmental Protection Agency (EPA) and have gathered data on the amount of waste generated in the United States each year. You want to develop models to predict the future amount of waste and the impact of recycling on reducing the amount of garbage.

Task

In this project you will play the part of a researcher for the EPA. You will look at data gathered by the EPA to determine how the amount of waste generated over time has changed and the impact of recycling on reducing this amount. Working together with your group, you will analyze data and make calculations to determine models for the amount of waste generated in the United States, the reduction of waste based on recycling, its’ cost to consumers, and the amount of landfills remaining.

Instructions

Solve each problem in order and save your work along the way, as you will create a professional report at the conclusion of the project.

· First problem: Solid waste generated per year

· The EPA has reported that in 1990 the United States generated 208.3 million tons of waste. In 2007 this amount had increased to 255.0 million tons. Assuming that the amount of solid waste generated is a linear function of time, find the slope (m) of this function.

[Hint: Slope (m) = ]

· To determine the function, you need to solve the following function for b (the y-intercept). Use the slope that you calculated, pick one of the two data points for W and t. Make sure that you calculate t as the number of years since 1990.

, where W is the amount of waste in millions of tons and t is time in years since 1990.

· What is the domain and range of the W(t) function? Explain what it means in terms of waste generated in the past and the future.

· Now, your group has a model to predict the amount of waste generated in the United States. Make predictions for 2010, 2020, 2030, and 2040.

t years since 1990	Predicted Amount of Waste Generated in the United States in millions of tons
20
30
40
50

· Second Problem: Impact of Recycling

· Another researcher at the EPA has developed the following model to predict the amount of recycled materials in millions of tons, R(t), as a function of time, t years since 1990.

Using the R(t) function, predict the amount of recycled materials for each year in the United States by filling in the following table:

t years since 1990	Predicted Amount of Recycled Materials in the United States in millions of tons
20
30
40
50

· If your group creates a new model of or , it will determine how much waste needs to be deposited in a landfill or incinerated. For convenience, call it landfill waste (L(t)). Determine this new model for landfill waste.

· Create a table of values for the landfill waste model. What is the domain and range? Using your table of values, create a graph of the landfill model. Explain how you think the amount of landfill waste will change over time.

t years since 1990	Landfill Waste, L(t) in millions of tons
0
10
20
30
40
50

· Third Problem: Cost of Waste Removal

· Experts give a range of different prices for the cost of waste removal depending on the location in the United States. The lowest price is $56.75 per ton and the highest price is $125.68 per ton. For each of the prices (low and high), determine the cost of waste removal for one million tons of waste.

· Next, your group will determine the total cost to remove the waste with both the low and high costs. Use the table from Part 2 for the amount of landfill waste and write your answer in terms of millions, billions, or trillions of dollars.

t years since 1990	Landfill Waste, L(t) in millions of tons	Total Cost of Waste Removal (Price of $56.75 per ton)	Total Cost of Waste Removal (Price of $125.68 per ton)
0
10
20
30
40
50

· Make a recommendation about the overall cost of removing waste. Include in your recommendation strategies for cities and states to cut costs.

· Fourth Problem: Number of Landfills

· In recent years, the EPA has been tracking the number of landfills in the United States. The pattern has been that the number of landfills is on the decline. A fellow researcher established the following model, N(t), for the number of landfills as a function of time:

with t = 2 corresponding to 1992.

Using the N(t) function, fill in the following table for various years over time.

t years since 1990	Number of Landfills, N(t)
2
5
10
15
20
25
30
35
40
45
50

· What is the domain and range of the N(t) function? Explain their significance.

· Sketch a graph of the N(t) function and state how the number of landfills will change over the next half-century (50 years).

Collaboration

Get together with another group to compare your answers to each of the four problems. Discuss how you might combine your answers to make a more complete and convincing analysis of the situation.

Conclusions

Present your solution in a way that makes it easy for the other researchers at the EPA to understand the significance of recycling and landfill closures. Be sure to clearly explain your reasoning at each stage and conclude with recommendations about waste generation, recycling, costs, and landfill closures. You should make a recommendation about how the waste generation business will change over the next 50 years.

Grade

Your project will be given a score of 1 to 4, with 4 being the highest score possible. Your project should correctly identify and justify mathematically: (1) waste generated linear function, (2) a simplified model for the impact of recycling, (3) the cost of disposing of solid waste, and (4) the graph of the decline in the number of landfills. You will be evaluated based on the following:

Score

Content

Presentation/Communication

• The solution shows a deep understanding of the problem including the ability to identify the appropriate mathematical concepts and the information necessary for its solution.

• The solution completely addresses all mathematical components presented in the task.

• The solution puts to use the underlying mathematical concepts upon which the task is designed and applies procedures accurately to correctly solve the problem and verify the results.

• Mathematically relevant observations and/or connections are made.

• There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.

• Mathematical representation is actively used as a means of communicating ideas related to the solution of the problem.

• There is precise and appropriate use of mathematical terminology and notation.

• Your project is professional looking with graphics and effective use of color.

• The solution shows that the student has a broad understanding of the problem and the major concepts necessary for its solution.

• The solution addresses all of the mathematical components presented in the task.

• The student uses a strategy that includes mathematical procedures and some mathematical reasoning that leads to a solution of the problem.

• Most parts of the project are correct with only minor mathematical errors.

• There is a clear explanation.

• There is appropriate use of accurate mathematical representation.

• There is effective use of mathematical terminology and notation.

• Your project is neat with graphics and effective use of color.

• The solution is not complete indicating that parts of the problem are not understood.

• The solution addresses some, but not all of the mathematical components presented in the task.

• The student uses a strategy that is partially useful, and demonstrates some evidence of mathematical reasoning.

• Some parts of the project may be correct, but major errors are noted and the student could not completely carry out mathematical procedures.

• Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.

• There is some use of appropriate mathematical representation.

• There is some use of mathematical terminology and notation appropriate of the problem.

• Your project contains low quality graphics and colors that do not add interest to the project.

• There is no solution, or the solution has no relationship to the task.

• No evidence of a strategy, procedure, or mathematical reasoning and/or uses a strategy that does not help solve the problem.

• The solution addresses none of the mathematical components presented in the task.

• There were so many errors in mathematical procedures that the problem could not be solved.

• There is no explanation of the solution, the explanation cannot be understood or it is unrelated to the problem.

• There is no use or inappropriate use of mathematical representations (e.g. figures, diagrams, graphs, tables, etc.).

• There is no use, or mostly inappropriate use, of mathematical terminology and notation.

• Your project is missing graphics and uses little to no color.

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Monterey Institute for Technology and Education 2011