Calculus project

MTH 1310 Project 2 Fall 2020

U.S. Coal Use

On blackboard, you will find a link to an excel file that shows Total Coal Production and Total Coal Consumption in the US for the years 1970-2017.

Import the data into Desmos and find two “best fit” curves to the data. One for Total Coal Production and one for Total Coal Consumption. To be as accurate as possible in the modeling, go ahead and use all decimal place values given in the regression model (up to as many as Desmos gives). I would like you to try the following models (2nd degree polynomial up to a 5th degree): Note below, that if your data is imported in your Desmos Table as x1, y1, then your models look like the following in Desmos. I did not use the letter e as a constant because e is a number like π and so you cannot use in that way.

y1 = ax 2 1 + bx1 + c

y1 = ax 3 1 + bx

2 1 + cx1 + d

y1 = ax 4 1 + bx

3 1 + cx

2 1 + dx1 + f

y1 = ax 5 1 + bx

4 1 + cx

3 1 + dx

2 1 + fx1 + g

1. Find the models for US Coal consumption and production. Write down your models and the R2

values. Which model is the “best fit” to the data and why? Provide a graph of ONLY the best fit curve to the data for each of the two models.

2. According to the models when did consumption and production peak? (Can you use derivatives to show this) Do the models accurately represent the data?

3. When do the models predict that consumption and production will be 0 metric tons?

4. How quickly was consumption and production decreasing in 2017 ( the last year of the data)?

5. If we assume consumption and production continue to decrease at the 2017 rates, then when will they reach 0 metric tons?

6. Summarize your results in a short paragraph and, in particular, include commentary regard- ing your predictions about when production and consumption will reach 0 metric tons. Incorporate information from this article in your summary: https://www.nytimes.com/2016/06/11/business/ energy-environment/coal-production-decline.html (This article is also posted on Blackboard for you if the link doesn’t work.) How would you need to update the NYT article given the information from this project?