Predicting the amount of plastic waste in landfills – by Shuangcheng

How big is the problem? Create a model for the amount of plastic that ends up in landfills in the United States. Predict the production rate of plastic waste over time and predict the amount of plastic waste present in landfills 10 years from today.

Flickr - Dan Butts photostream

Flickr – Dan Butts photostream

When I was thinking about this question in the Moody’s Math Challenge, Markov Chain initially came into my mind. Markov Chain was first introduced to me in my Linear Algebra at Westtown School class last year as an application of a matrix in the real world. According to the Linear Algebra textbook, the Markov Chains are used as mathematical models of a wide variety of situations in biology, business, chemistry, engineering, physics, and elsewhere. In each case, the model is used to describe a transformation that is performed many times in the same way, where the outcome of each transformation depends only on the immediately preceding one.

The reason that we considered using Markov chain in our situation is that we had found data online that said that the annual recycling rate for plastic wastes is approximately 5%.  Now thinking back, Markov chain might not be the best option since in the real cases each year’s recycling rates are constantly changing instead of remaining the same. It means that when we chose the Markov Chain, we were assuming that starting from 2012 to the next 10 or 100 years the recycling rate is remaining at 5% for the plastic wastes. And so in my new paper for Question 1, I will focus more on the growing and changing rate of recycling and focus on what data say.

What I am working on now is considering the factor of population growth. The concept of population has never occurred to me before. The amount of landfilled plastic waste will be largely related to the American population in ten years. Below is my data collection for the American populations:

Years American Population (millions)
2011 3166
2010 3093
2009 3068
2008 3041
2007 3012
2006 2984
2005 2955
2004 2928
2003 2901
2002 2876
2001 2850
2000 2822
1999 2790
1998 2759
1997 2726
1996 2694
1995 2663
1994 2631
1993 2599
1992 2565
1991 2530
1990 2496
1989 2468
1988 2445
1987 2423
1986 2401
1985 2379
1984 2358
1983 2338
1982 2317
1981 2295
1980 2265
1979 2251
1978 2226
1977 2202
1976 2180
1975 2160
1974 2139
1973 2119
1972 2099

It is well known that we use exponential equations as the population model. Then I could use a data-analyzing tool such as Excel to form an exponential equation for the American population, which will lead me to the American population in 10 years and 100 years (although I will have more to say about this).

Then I focused on the data for the amount of plastic waste landfilled. Below are my data:

Years Amount of Plastic Waste landfilled (Thousand tons)
2011 29190
2010 28490
2009 27710
2008 27930
2007 28640
2006 27450
2005 27260
2004
2003 25260
2002
2001 23990
2000 23370
1999 23360
1998 20350
1997 18700
1996 17990

In the short term, or in this case, ten-year-time, the data reveal a linear growth, and so I think that I would go with a linear function for the estimated amount in ten years. In 100 years, however, it would be a totally different story. People begin to emphasize more about the idea of ecological economy, which will provide incentives to find alternative ways for landfill. Technology breakthroughs, which would seem improbable in a ten-year-period, would absolutely happen in the next 100 years. Therefore, if I have to make a prediction for 100 years later with a number and a function, I will choose a logarithmic tendency at the beginning and then switch to a declining function.

Hopefully, this part of the problem will be done in a week or two.

Shuangcheng Du

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