##### Exercise5

Suppose we have the female population of a species is divided into juveniles, yearlings, and adults and that each year

• 90% of the juveniles live to be yearlings.

• 80% of the yearlings live to be adults.

• 60% of the adults survive to the next year.

• 50% of the adults give birth to a juvenile.

1. Set up a system of the form $$\xvec_{k+1}=A\xvec_k$$ that describes this situation.

2. Find the eigenvalues of the matrix $$A\text{.}$$

3. What prediction can you make about these populations after a very long time?

4. If the birth rate goes up to 80%, what prediction can you make about these populations after a very long time? For every 100 adults, how many juveniles, and yearlings are there?

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