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. Set up a system of the form xk+1=Axk that describes this situation. Find the eigenvalues of the matrix .A. 1 Evaluate (Sage) What prediction can you make about these populations after a very long time?

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. Set up a system of the form xk+1=Axk that describes this situation. Find the eigenvalues of the matrix .A. 1 Evaluate (Sage) What prediction can you make about these populations after a very long time?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 30E

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5.

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.

Set up a system of the form xk+1=Axk that describes this situation.
Find the eigenvalues of the matrix .A.

1

Evaluate (Sage)
What prediction can you make about these populations after a very long time?
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?