Will Our Earth Turn into a “Plastic Planet”? : Analysing The Trend Using Quadratic Function

Plastic Planet (source: www.youtube.com)

Do you familiar with plastics? Everywhere plastics can be found in our daily activities. When you buy food or drink, plastic is used as its container. When you go to the market, plastic is used to put in groceries. Regarding that, plastics can be assumed as our friend. However, when you throw plastics away, plastics became a heap of waste that is difficult to decipher. Can you predict what is the effect of that, if everyone in this world still keeps using plastics? Is it true that our earth turns into a plastic planet? To predict the problem, a method that can be used is by analyzing the quadratic trendline. But first, do you still remember what is Quadratic Function, and how to use the quadratic function in predicting the production of plastics? Let’s investigate!

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. The picture below is a basic graph of quadratic function f(x) = x2.

Look at the left picture! The graph on the right side of the y-axis is increasing. If we compared to the data from ourworldindata.org in the right picture, the graph of global plastics production is similar to the graph of quadratic functions. Both are concave upward and have the form of f(x) = ax2 + bx + c.Therefore, we can use the concept of quadratic functions to solve the problem. In the function of f(x) = x2 , the number of a is 1 and the number of b is 0. For the production of plastics function, we need to find the number of a, b, and c. In other words, the exact function of plastic products should be found. However, the actual data are not well-ordered or not fit the general form. The graph of the actual data looks like the picture below. So, analyzing the quadratic trendline will help us to obtain the function of plastics production that fit with general form. Afterward, we can predict the number of plastics in the next few years.

Source: https://ourworldindata.org/plastic-pollution

Generally, a quadratic trendline is a second-order polynomial which attempts to best fit a set of data. Quadratic trend lines allow us to predict the possible events in the future. To obtain the quadratic trendlines, translating the data to Microsoft Excel is required. There are many ways to do a trendline, but this is a simple and common way to do that. First, make a table in Microsoft Excel to show the data like the picture below. Let’s assume X is xth year of plastic production from 2010, and f(x) is the number of plastics production in million tons.

Table of plastics production data

After that, make a quadratic trend line using the data in the table. Here we get the graph. The blue line is a graph based on the actual data, and the red line is a trend line. From this graph, we get the function of the number production of plastics f(x) = 0.069x2–266.14x + 256290.

Based on the function, the number of plastics production in 2020 is around 430 million tons. This number will increase as the use of plastic is also increase. Can you imagine how much the total number of plastics that are produced in this world? This probably makes our world is full of plastics, and turn our earth into the plastic planet. It will cause many negative impacts on our life. By analyzing the trend of plastics production using a quadratic function, we are able to predict plastic production. Based on the result, we know that plastics production will increase. So from now on, let’s reduce the use of plastics. This can reduce the production of plastics, and make our earth save.

References:

https://ourworldindata.org/plastic-pollution

http://dl.uncw.edu/digilib/Mathematics/Algebra/mat111hb/PandR/quadratic/quadratic.html

https://flintanalytics.com/math-for-marketers-quadratic-trendlines/

https://www.techadvisory.org/2014/05/what-is-analysis-with-trendlines/

I am a Mathematics Education Student at Sampoerna University