Carbon dioxide concentrations (in parts per million) have been measured directly from the atmosphere since 1960. This concentration has increased quadratically. The table lists readings for three years.

(a) If the quadratic relationship between the carbon dioxide concentration C and the year t is expressed as C = at² + bt + c, where t = 0 corresponds to 1960, use a system of linear equations to determine the constants a, b, and c, and give the equation.

(b) Predict when the amount of carbon dioxide in the atmosphere will be double its 1960 level.

Year …………………….Co₂

1960 ……………………317

1980 ……………………339

2013 ……………………396