Assumptions:

1. The generations are distinct (making this a discrete system).

2. Each rabbit pair will be ready to reproduce at the end of the second generation (born in Generation 1, develop in Generation 2, first offspring in Generation 3).

3. Each pair of mature rabbits has one pair of offspring in each generation.

4. Rabbits will live forever. The model does not assume that there is a life expectancy for rabbits.

5. Rabbits will continue to have offspring forever. The model does not assume that rabbits will stop having offspring after a certain number of generations.

Task A

Keeping all assumptions from the model in Part 1, answer the question "In which generation does the rabbit population reach a level of 100,000 pairs of rabbits?" Be sure to build the model into a spreadsheet (as we did in Part 1).

Task B

Now let us change assumption 2 and instead assume that rabbits do not have offspring until the 4th generation (instead of the 2nd). Create another rabbit model to answer the question "In which generation does the rabbit population reach a level of 100,000 pairs of rabbits?" under this modified assumption. Be sure to give an algorithmic description of this model in terms of a recurrence relation and also build your model into a spreadsheet.

Task C

Now go back to the original model from Part 1 and change assumption 3. Let's assume that rabbits have 2 pairs of offspring each time instead of one pair. Create another rabbit model to answer the question "In which generation does the rabbit population reach a level of 100,000 pairs of rabbits?" under this modified assumption. Be sure to give an algorithmic description of this model in terms of a recurrence relation and also build your model into a spreadsheet.

Task D

Now go back to the original model from Part 1 and change assumption 4. Let's assume that rabbits die after 5 generations instead of living forever. Create another rabbit model to answer the question "In which generation does the rabbit population reach a level of 100,000 pairs of rabbits?" under this modified assumption. Be sure to give an algorithmic description of this model in terms of a recurrence relation and also build your model into a spreadsheet.