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]

Shrinking Species

Since 1800, the number of amphibian species, N, has been decreasing over time, t. 

A simple model shows that the rate of decrease of the number of species is proportional to the remaining number of species.

Given that the initial number of amphibian species is N0, and t is the number of years since 1800,

a) Show that \(N = N_{0}e^{- kt}\)

[4 marks]

In 2000 the number of amphibian species is 0.9N₀.

b) Find the exact value of k.

[3 marks]

c) Using the model, in what year will 20% of amphibian species be
extinct?

[3 marks]

Surviving Species

Climate change affects the habitats and environments of many species, some of which won’t be able to adapt fast enough to survive in their new habitats.

The graph shows the percentage of species driven extinct since 1500. Of the species that were around in 1500

Diagram showing Extinctions since 1500

a) Calculate the probability of a reptile species having gone extinct by 1900. 

[1 marks]

b) Calculate the probability of an amphibian species not having gone extinct by 2018. 

[1 marks]

c) Of a sample of 60,000 species alive in 1500, assuming equal numbers of amphibian, mammal, bird, reptile and fish species are included, find, by first taking an average, how many species you would expect to have not gone extinct by 2018.

[3 marks] 

Reducing Biodiversity Loss

The graph from the IPBES Global Assessment Report on Biodiversity and Ecosystem Services shows 3 different scenarios for how we could reduce biodiversity loss by 2050. Each scenario prevents the same amount of biodiversity loss.

graph from the IPBES Global Assessment Report on Biodiversity and Ecosystem Services

a) Look at the Global Technology scenario. What is the biggest measure that would be taken in this scenario? 

[1 mark]

b) Look at all three scenarios together. Which scenario would involve reducing infrastructure expansion the most? 

[1 mark]

c) What measure would be taken in the Consumption Change scenario that would not be taken in the scenarios of Global Technology or Decentralised Solutions? 

[1 mark]

d) Using a ruler, work out the percentage decrease of increasing agricultural productivity when comparing the scenario of Global Technology to Decentralised Solutions. 

[3 marks]

Extinct Species Per Degree

Climate change can lead to species extinction through changing habitats rapidly, not leaving the species time to adapt. Warming at the moment is at 1°C.

A study of 105000 species suggests that for each extra 1°C of warming above pre-industrial temperatures, 9% of species will become extinct.

For example, at a warming of 3°C, 9% of species still in existence at a warming of 2°C will have gone extinct.

Work out the number of species that have not gone extinct at a warming of 4°C.

Give your answer to 2 significant figures.

[4 marks]

Rainforest Reforestation

One way of reducing carbon dioxide in the atmosphere and slowing global warming is to plant trees which absorb carbon dioxide from the atmosphere.

A scientist plants some trees in the Amazon rainforest and the Tongass rainforest.

The scientist compares the carbon dioxide absorbed from the atmosphere by the trees she planted in the Amazon rainforest with the trees she planted in the Tongass rainforest.

Amazon

Carbon absorbed per tree

\(\frac{1}{5}\) more than in the Tongass

Number of trees planted

\(\frac{1}{4}\) less than in the Tongass

By what fraction is the total carbon dioxide absorbed by the trees planted in the Amazon compared with the total carbon dioxide absorbed by the trees planted in the Tongass rainforest? 
[3 marks]

Losing Coral Reefs

don't use calculatorGlobal warming will affect the world’s coral reefs.

In a world heated by a global warming of 2°C, we will lose 99% of coral reefs.

In a world heated by a global warming of 1.5°C, we will lose 81% of coral reefs.

Express the percentage of coral reefs lost in a world warmed by 2°C  as a fraction of the amount of coral reefs lost in a world warmed by 1.5°C. Give your answer in its simplest form.

[2 marks]

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