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A Quadratic Emissions Model

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The graph shows the rate of CO2 emissions per year since 1800.

Global Carbon Dioxide Emissions Graph

A climate scientist thinks that a quadratic curve could be fitted to the data, where the x axis is years since 1800, and the y axis is the rate of CO2 emissions per year (GtCO2 year-1). 

This curve would be of the form \(y = Ax^{2} + Bx + C\).

a) By using the points (166 , 42), (106 , 14) and (10 , 3), taken from the best fit lines on the graph shown above, evaluate the coefficients A, B, and C  in this model.

[4 marks]

b) By finding the minimum point of the curve, assess the suitability of this model as a fit for the data.

[3 marks]

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