The graph shows the rate of CO_{2} emissions per year since 1800.

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 CO_{2} emissions per year (GtCO_{2} 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**,

**, and**

*B***in this model.**

*C*[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]