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A Carbon Negative Company

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A small company’s carbon dioxide (CO₂) emissions since 2000 can be modelled using the parametric equations

\[12x = t,\ y = 8t – 4.9t^{2} + 10,\ t \geq 0\]

Where x is the number of years since 2000 and y the yearly CO₂ emissions, in tonnes. 

Due to an afforestation program, the company’s emissions can go negative, as the trees planted absorb CO₂ from the atmosphere. 

a) Find the year in which the company’s CO₂ emissions go negative.

[4 marks]

b) Find the greatest amount of CO₂ emissions from that company in one year

[5 marks]

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