9. The adult population of a town is 25000 at the end of Year 1.
A model predicts that the adult population of the town will increase by \(3 \%\) each year, forming a geometric sequence.
- Show that the predicted adult population at the end of Year 2 is 25750.
- Write down the common ratio of the geometric sequence.
The model predicts that Year \(N\) will be the first year in which the adult population of the town exceeds 40000.
- Show that
$$( N - 1 ) \log 1.03 > \log 1.6$$
- Find the value of \(N\).
At the end of each year, each member of the adult population of the town will give \(\pounds 1\) to a charity fund.
Assuming the population model,
- find the total amount that will be given to the charity fund for the 10 years from the end of Year 1 to the end of Year 10, giving your answer to the nearest \(\pounds 1000\).