8. A trading company made a profit of \(\pounds 50000\) in 2006 (Year 1).
A model for future trading predicts that profits will increase year by year in a geometric sequence with common ratio \(r , r > 1\).
The model therefore predicts that in 2007 (Year 2) a profit of \(\pounds 50000 r\) will be made.
- Write down an expression for the predicted profit in Year \(n\).
The model predicts that in Year \(n\), the profit made will exceed \(\pounds 200000\).
- Show that \(n > \frac { \log 4 } { \log r } + 1\).
Using the model with \(r = 1.09\),
- find the year in which the profit made will first exceed \(\pounds 200000\),
- find the total of the profits that will be made by the company over the 10 years from 2006 to 2015 inclusive, giving your answer to the nearest \(\pounds 10000\).