Home » Maths for Planet Earth » Shrinking Species

# 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]

## More Maths for Planet Earth

A Level
##### Colliding Currents
2 deep sea ocean currents meet. By modelling one current as the positive y axis. a) Find the angle that the second current, with
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
GCSE
##### Allotment Areas
A citizen wants to reduce their carbon footprint, so decides to grow their own produce in their garden. The area set out for growing
GCSE
##### Graphing the IPCC Carbon Dioxide Predictions
This graph, from the IPCC 1.5°C report, shows how the rate of carbon dioxide emissions varies with time in two scenarios in which global