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]