Home » Maths for Planet Earth » City Emission Levels

# City Emission Levels

The emissions of a city from 2000 to 2012 are modelled by the equation

$$p\left( t \right) = \frac{1}{10}\ln\left( t + 1 \right) – \cos\frac{t}{2} + \frac{1}{10}t^{\frac{3}{2}} + 199.3$$

$0 \leq t \leq 12$

a) Show that the emissions reach a local maximum in the interval $$8.5 \leq t \leq 8.6$$

[5 marks]

The emissions reach a local minimum between 9 and 11 years after the measurements began.

b) Using the Newton-Raphson procedure once and taking $$t_{0} = 9.9$$ as a first approximation, find a second approximation of when the emissions reach a local minimum.

[6 marks]

## More Maths for Planet Earth

A Level
##### A New Renewable
A scientist wishes to develop a new way of generating renewable energy. They decide to use a large magnet on a large spring, oscillating
A Level
##### Colliding Currents
2 deep sea ocean currents meet. By modelling one current as the positive y axis. a) Find the angle that the second current, with
GCSE
##### Decreasing Fish Stocks
Global warming will affect the world’s annual fishing catch. In a world heated by a global warming of 2°C, the annual fishing catch will
A Level
##### A Solar Sine Curve
You are given the equation [fleft( x right) = 5costheta – 8sintheta] a) Express f(x) in the form (Rcos{(theta + alpha})) where (R >