Home » Maths for Planet Earth » A Regrowing Reef

A Regrowing Reef

Facebook
Twitter
Pinterest
Print

a) Use the substitution \(u = 4 – \sqrt{s}\) to show that

\[\int_{}^{}\frac{\text{dh}}{4 – \sqrt{s}} = – 8\ln\left| 4 – \sqrt{s} \right| – 2\sqrt{s} + k\]

where k is a constant

[6 marks]

 

A coral reef is growing back after global temperatures are reduced from their peak value.

The rate of change of area covered by the reef is modelled by the differential equation

\[\frac{\text{ds}}{\text{dt}} = \frac{t^{0.25}(4 – \sqrt{s})}{20}\]

Where s is the surface area of the reef in m2 and t is the time, in years, after the reef begins to regrow.

b) Find, according to the model, the range of areas that could be covered by the coral reef. 

[2 marks]

The coral reef has a surface area of 1m2 when it starts to regrow.

According to the model,

c) Calculate the time this reef would take to cover 12 m2, giving your answer to 3 significant figures.

[7 marks]

Start exploring

Latest from blog

More Maths for Planet Earth

GCSE
The graph below shows how the rate of carbon dioxide emissions varies from 1800 to 2020. By using the appropriate lines of best fit
GCSE
The increasing global temperature due to human-induced climate change is causing ice in the Arctic to melt, particularly over the summer season, July to
GCSE
Carbon capture and storage is method of removing carbon dioxide from the atmosphere and storing it as a liquid underground. Carbon capture and storage
GCSE
Cars and transport, and the gases and particulates that they emit from their exhausts have a serious effect on the environment and on human