A Shrinking Rainforest

  1. In a simple model, the surface area, S km2, of a shrinking rainforest depends on the time, t, in years since 1980.

The following information is available for rainforest A.

  • its surface area in 1980 was 300,000 km2
  • its surface area in 1981 was 294,000 km2
a) Use an exponential model to form, for rainforest A, a possible equation linking S with t.

[4 marks]

The surface area of rainforest A is monitored over a 30-year period. Its surface area after 30 years is 150,000 km2.

b) Evaluate the reliability of your model in light of this information.

[2 marks]

The following information is known about rainforest B.

  • it had the same surface area, in 1980, as rainforest A
  • it is harder to access by road, so the rate of deforestation is less than rainforest B and its surface area decreases more slowly than that of rainforest A
c) Explain how you would adapt the equation found in (a) so that it could be used to model the surface area of rainforest B.

[1 mark]

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] 

A Cocoa Catastrophe

Chocolate is made from a crop called cocoa, which grows on a tree. Cocoa trees are vulnerable to extreme weather events such as floods and droughts, which means that more and more cocoa trees do not successfully produce cocoa each year. 

The number of cocoa trees in a plantation that are still producing cocoa is given by

\[C = 16500\ \times {0.82}^{n}\]

where \(n\) is the number of years after the cocoa trees are first planted.

a) Write down the number of cocoa trees first planted.

[1 mark]

b) Write down the annual percentage decrease of cocoa trees.

[2 marks]

c) Show that the number of successful cocoa trees after 4 years is less than half the number of trees first planted.

[2 marks]