# 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:

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.

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?