Please help answer questions.
The debate around global warming has been a hotly contested one in recent years in both the scientific and wider communities. Both sides of the argument often cite scientific research to support their point of view; the majority of this research relies on effective data analysis. In this part of the assignment you are going use some of the major concepts we have seen within the topic of Calculus to analyse some data that can be used as evidence for or against global warming, 'Global Tempearture Anomalies'. "In climate change studies, temperature anomalies are more important than absolute temperature. A temperature anomaly is the difference from an average, or baseline, temperature. The baseline temperature is typically computed by averaging 30 or more years of temperature data. A positive anomaly indicates the observed temperature was warmer than the baseline, while a negative anomaly indicates the observed temperature was cooler than the baseline." Courtesy of National Oceanic and Atmospheric Administration (NOAA, USA) The scatter plot on the next page displays the Global Temperature Anomoly for each year from 1750 until 2017. For the purposes of calculation the horizontal axis is measured in years since 1750 (it starts at 0 and goes up to 267, since 2017-1750 = 267). The baseline temperature for each year is dynamic, as it is a 'rolling average' of the global average temperature from 1750 until the year of interest. For instance, the temperature anomaly for the year 1995 (which is 245 years since 1750) is +0.73, which means the global average temperature in 1995 was 0.73'C hotter than the overall average temperature from 1750 until 1995. It is customary to approximate the data within a scatterplot using a 'trendline'. The converting of the scattered points into a uniform line allows for more extensive analysis and predictions. The trendline for the scatterplot below is a polynomial of degree 4 and has the formula: A(t) = (9 x 109)* - (4.89 x 10-6)13 + (9.03 x 10-4)2 - 0.0606t + 0.62 Global Temperature Anomalies for the years 1750 - 2017 2.50 2.00 A(t) = (9 * 10 9)+4 - (4.89 x 10-6)+3 + (9.03 x 10-4)2 - 0.0606t + 0.62 1.50 1.00 0.50 0.00 Global Temperature Anomaly (" -0.50 1.00 1.50 -2.00 -2.50 50 100 150 200 250 300 Time (Years since 1750) Questions: (20 marks total) 1) Determine the equation of the gradient function for the trend line. (1) 2) Graph the trendline using desmos or other graphing software (you are not required to submit an image of the graph). Using the software, identify: a. The coordinates of any turning points (2) b. The range of years for which the temperature anomaly is: i. Increasing (1) ii. Decreasing (1) Interpret the values calculated in Question 2. (3) 4) Use the equation of the trendline to calculate the average rate of change between the years 1750 - 1960. (2) 5) Use the equation of the trendline to calculate the average rate of change between the years 1960 - 2017. (2) 6) Compare your results from Question 4 and Question 5. Interpret any differences and explain how this could be used as evidence for or against climate change. (2) 7) Predict the rate at which the global temperature will be changing in the year 2041 (20 years from now). (2)
