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?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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 xk+1=Axk that describes this situation.

  2. Find the eigenvalues of the matrix .A.

     
     
     
     
     
    1
     
     
     
    Evaluate (Sage)
     
     

     

  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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