Home » Maths for Planet Earth » A Carbon Conscious Company

A Carbon Conscious Company

The curve

\[y = e^{-0.5x} + 4x – 0.1x^{2} + 2\]

Can be used to describe a company’s net emissions, in tons of CO2, x decades after 2000. 

a) By first using calculus, show that peak emissions occur at 19 ≤ x ≤ 21

[4 marks]

The company owns an afforestation program. As trees absorb CO2, this means that their net emissions can decrease to negative values.

b) Show that the emissions become negative between 39 and 41 years after the year 2000.

[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 x0 = 39

[4 marks]

Start exploring

Latest from blog

More Maths for Planet Earth

A Level
In a simple model, the surface area, S km2, of a shrinking rainforest depends on the time, t, in years since 1980. The following
A Level
The graph shows the rate of CO2 emissions per year since 1800. A climate scientist thinks that a quadratic curve could be fitted to
Here is a pie chart taken from Mike Berners-Lee’s book There is no Planet B.  a) Calculate angle x. (shown on graph in the
A Level
The height (h km) that a weather balloon can reach is related to the volume (v m₃) of helium in it at sea level