Here's the problem

The growth of a certain population is modelled by the recursion formula

and

,

for n

1, where

is the size of the population after period k.

I have already done the first part which is to show by induction that it is strictly increasing. The next part is

Make a conjecture for a formula for

, and prove it by induction. Hint: Consider the difference between

and some suitable upper limit.

How do I go about that? Will the formula be something like

= 6000+something to the power of n? Any help appreciated thank you.