Home » Maths for Planet Earth » A Regrowing Reef

# A Regrowing Reef

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]

## More Maths for Planet Earth

A Level
##### Net-Zero Buses
15 cities, each of varying sizes, decide to have carbon-neutral public transport systems. When the cities are arranged in size order from smallest to
A Level
##### Wiring up a Net-Zero Home
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
##### A Desert Area Increase
Climate change (or global warming) can cause the areas of deserts (very dry land) to increase, affecting the surrounding wildlife and ecosystems. Before global
A Level
##### A Speedy Sea Current
An ocean current separates into 2 different currents at a small island that can be modelled as the origin. Current A heads due south