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] 

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]