9. David has been investigating the population of rabbits on an island during a three-year period. Based on data that he has collected, David decides to model the population of rabbits, \(R\), by the formula $$R = 50 \mathrm { e } ^ { 0.5 t }$$ where \(t\) is the time in years after 1 January 2016.

1. Using David's model:
2. 1. state the population of rabbits on the island on 1 January 2016;
3. (ii) predict the population of rabbits on 1 January 2021.
4. Use David's model to find the value of \(t\) when \(R = 150\), giving your answer to three significant figures.
5. Give one reason why David's model may not be appropriate.
   [0pt] [1 mark]
6. On the same island, the population of crickets, \(C\), can be modelled by the formula $$C = 1000 \mathrm { e } ^ { 0.1 t }$$ where \(t\) is the time in years after 1 January 2016.
   Using the two models, find the year during which the population of rabbits first exceeds the population of crickets.
   [0pt] [3 marks]