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)|
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)|
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.