- In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
The number of dormice and the number of voles on an island are being monitored.
Initially there are 2000 dormice on the island.
A model predicts that the number of dormice will increase by \(3 \%\) each year, so that the numbers of dormice on the island at the end of each year form a geometric sequence.
- Find, according to the model, the number of dormice on the island 6 years after monitoring began. Give your answer to 3 significant figures.
The number of voles on the island is being monitored over the same period of time.
Given that
- 4 years after monitoring began there were 3690 voles on the island
- 7 years after monitoring began there were 3470 voles on the island
- the number of voles on the island at the end of each year is modelled as a geometric sequence
- find the equation of this model in the form
$$N = a b ^ { t }$$
where \(N\) is the number of voles, \(t\) years after monitoring began and \(a\) and \(b\) are constants. Give the value of \(a\) and the value of \(b\) to 2 significant figures.
When \(t = T\), the number of dormice on the island is equal to the number of voles on the island. - Find, according to the models, the value of \(T\), giving your answer to one decimal place.