# 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

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

This site uses Akismet to reduce spam. Learn how your comment data is processed.