\[y = e^{-0.5x} + 4x – 0.1x^{2} + 2\]

Can be used to describe a company’s net emissions, in tons of CO_{2}, *x* decades after 2000.

*x*≤ 21

[4 marks]

The company owns an afforestation program. As trees absorb CO_{2}, this means that their net emissions can decrease to negative values.

[2 marks]

c) Use the Newton-Raphson method to find, to 4 significant figures, the number of decades it takes for the emissions to become negative. Use

*x*

_{0}

*= 39*[4 marks]