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Using Polynomial Differentiation to Analyze Global Atmospheric CO2

Classroom/Laboratory Activity

A classroom/laboratory activity to learn and apply polynomial differentiation and to solve tangent line problems for global average CO2 data.

Students will observe the trend in increasing atmospheric CO2 levels, infer when atmospheric CO2 levels could cause global temperatures to increase by 2 °C (potentially leading to serious climate-change related problems), and determine rates of change of CO2 levels by performing polynomial differentiation and solving tangent line problems. They will use atmospheric CO2 data from the Mauna Loa site for the period 1950 to 2017.

Use this tool to help your students find answers to:

  1. Plot a graph and find the polynomial equation to model the average yearly atmospheric CO2 levels from 1950 to 2017 (using data records provided).
  2. Compare and analyze the rate of change of atmospheric CO2 levels by applying Polynomial Differentiation.
  3. Based on observed trends, what will the atmospheric CO2 level be in 2100?
About Tool
Tool Name Mauna Loa Yearly Average CO2 
Discipline Mathematics and Statistics
Topic(s) in Discipline Functions, Calculus, Differentiation, Polynomial Differentiation, Tangent Line Problem 
Climate Topic Climate and the Anthroposphere, Climate Variability Record
Type of tool Classroom/Laboratory Activity 
Grade Level High School, Undergraduate
Location Global
Language English
Translation      –
Developed by Thomas J. Pfaff, Ithaca College 
Hosted at Sustainability Math
Access Online/Offline 
Computer Skills Basic


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