In which year do profits exceed 200,000 in the following case?A trading company made a profit of 50000 in year 1. The future profits are predicted...

We are given that the company makes profits of 50,000 in
the first year and they are predicted to increase every year in such a manner that a
geometric series is formed. As the common ratio is r, the profits in year 2 are
50,000*r, in year 3 they are 50,000*r^2 and so on. In year n the profits are 50000*r^(n
- 1)

If profits exceed 200,000 in the year n, we
have

50000*r^(n - 1) >
200000

divide both sides by
50000

=> r^(n - 1) >
4

take the log of both the
sides

=> (n - 1)* log r > log
4

=> n - 1 > (log 4)/(log
r)

=> n > [(log 4)/(log r)] +
1

This gives the year n in which profits
exceed 200000, one where n > [(log 4)/(log r)] +
1