Home » Maths for Planet Earth » Ice Incineration

Ice Incineration

Facebook
Twitter
Pinterest
Print

A country’s government wants to reduce the number of cars using internal combustion engines by encouraging the purchase of electric vehicles.

The total number of cars using internal combustion engines in a country at time t can be modelled by the equation

\[N\left( t \right) = \left( 3.5 \times 10^{7} + E \right)e^{- \frac{1}{10}t} – E\]

Where N(t) is the number of cars using internal combustion engines at time t years after the program was introduced and E is the number of electric vehicles on the roads before the government initiative.

Using the equation for this model,

a) Explain the significance of the number 3.5 x 107.

[1 mark]

 

b) Explain why the initial number of cars using internal combustion engines is independent of the initial number of electric vehicles.

[2 marks]

c) Calculate the number of cars using internal combustion engines after 10 years if the initial number of electric vehicles is 2 x 106.

[2 marks]

d) Analyse the suitability of this model by evaluating it for large values of t.

[2 marks]

Start exploring

Latest from blog

More Maths for Planet Earth

GCSE
The table gives information about how the UK used its energy in 2017. CREDS calculations based on BEIS (2018) Sector Percentage of UK energy
A Level
A homeowner decides to make their house carbon-neutral. They place solar panels on the roof, which then connect o their mains circuit via a
GCSE
The table shows information about sea level rise due to human-induced climate change. (mm = millimetres). Sea level rise in 2006 (mm) Sea level
BACK TO TOP