9. The resident population of a city is 130000 at the end of Year 1
A model predicts that the resident population of the city will increase by \(2 \%\) each year, with the populations at the end of each year forming a geometric sequence.
- Show that the predicted resident population at the end of Year 2 is 132600
- Write down the value of the common ratio of the geometric sequence.
The model predicts that Year \(N\) will be the first year which will end with the resident population of the city exceeding 260000
- Show that
$$N > \frac { \log _ { 10 } 2 } { \log _ { 10 } 1.02 } + 1$$
- Find the value of \(N\).