Using Matlab: Rabbits of the Fibonacci variety: Rabbits reproduce very quickly. Lets assume that an adult pair of rabbits gives birth to one new pair of baby rabbits every month, a male and a female. Well also assume that it takes one month for the baby rabbit to become an adult, and one months gestation time between the time a pair of rabbits becomes adult and the time their first pair of offspring are born. For the purposes of this model, we assume that rabbits never die. To start, we have a female and male baby rabbit.

1. Introduce notation and come up with a difference equation that describes this simple model.

2. Graph the number of rabbits after a fixed number of months.

3. Find a function f(t), where t is any real number, that best fits the output of the difference equation.

4. Modify your model to make it more realistic (general gestation period, rabbit death, rabbits can only produce for k months, etc.)

Write-Up: No longer than two pages. Guidelines:

1. Description of the problem: Be sure to include any assumptions youve made, and be specific.

2. Description of the model: Introduce notation and variables you will be using. Explain how the model works and how you implemented the model in Matlab.

3. Data and results: Provided a summary of your results with at least one graph or table sup- porting your findings.

4. Improvements: Implement into the model at least one improvement and discuss the impact of this change on the results.

5. Conclusion: Briefly summarize the problem and your results and discuss limitations of the model and/or further improvements.