Complete Moody’s Paper Question 1 — Shuangcheng Du

This week I wrapped up my solution for question 1 in last year’s Moody’s Math Challenge with some more thoughts coming up and more time writing them down. Just as a reminder I will repost the question 1 below:

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.

As I mentioned in earlier blog post, I have shifted my focus to using the idea of American population growth and the amount of plastic waste landfilled per capita. To me, it is the idea of involving amount per capita that is the key to my thoughts in this question. It is common sense to me that everywhere people around us are discarding approximately the same amount of plastic everyday. Therefore, it is reasonable to calculate out the amount of plastic waste landfilled per capita in recent years and to create a model according to the trend that data shows.

Years Amount of Plastic Waste landfilled per Capita (kg)
2011 9.219835755
2010 9.211121888
2009 9.031942634
2008 9.18447879
2007 9.508632138
2006 9.199061662
2005 9.225042301
2004
2003 8.707342296
2002
2001 8.41754386
2000 8.281360737
1999 8.372759857
1998 7.375860819
1997 6.859867938

According to the data above, a scatter graph is shown with Excel:

Moody 1

The trend I see in this graph is Logarithmic, and the function I get for the trend-line is

y = 285.83ln(x) – 2164.5

Therefore, inserting x=2023 and x=2113 to predict the amount (kg) of plastic waste landfilled per capita in 10 years and 100 years. When x=2023, y=11.3342; when x=2113, y=23.7756

Then I start to consider the model for American Population Growth

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

Above are the data for last 30 years. I then insert all the data into Excel and get a scatter graph with an exponential function on it.

Moody 2

The function of our model is y = 2E-06e0.0105x’;

When x=2023, y=3358.12 (Millions); When x=2113, y=8639.82 (Millions)

Then I can get the prediction on the amount of plastic waste landfilled in 10 years and 100 years:

In 10 years, it will be 38061.6 thousand tons.

In 100 years, it will be 205416.9 thousand tons.

Now at the end of my prediction for 100 years, it is crucial for me to state that 100 year prediction is in fact unpredictable. With many great potential technology breakthroughs coming into our life, it is indeed hard to say either what our population in 100 years would be like, or how much is the amount of plastic waste landfilled.

One thought on “Complete Moody’s Paper Question 1 — Shuangcheng Du

  1. margaretjhaviland

    Now you have your model for stasis, if nothing changes other than the population. So assume an intervention, create an intervention. How will you create a means for Americans to reduce the amount of plastic in our landfills. Is it enough for us to try and recycle our way out of 38061.6 thousand tons in ten years?

    Reply

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