 # 1. Find the fixed points of the following recurrence relation, and ...

## Question

1. Find the fixed points of the following recurrence relation, and determine if each fixed point is stable or unstable: x (n)=( x(n−1))²−x(n−1)−3 , n = 1, 2, 3, ...
2. Find a closed form solution for the following second order recurrence relation: x (0)=1, x (1)=−14 , and x (n)=2 x (n−1)+8 x (n−2) for n = 2, 3, 4, …
3. Suppose a bird population grows at rate r (in decimal form) annually. In addition, H birds are hacked each year, and P percent (in decimal form) of the population is harvested each year.
(a) Sketch a compartmental diagram for the size of the population.
(b) Write a difference equation (or recurrence relation) for this model.
4. Suppose an insect population is currently 500 individuals, the annual birth rate is 28.6%, the annual death rate is 4.5%, and 200 insects are removed each year. Determine if the insect population will stabilize at a positive number, if it will go to zero, or if it will grow infinitely large. If it will stabilize at a positive number, what will the stable population be? Explain your answers

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