Here's the problem
The growth of a certain population is modelled by the recursion formula
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.