9. The local Pacific green sea turtle reaches maturity at age 24 and has a lifespan of about 70 years. So we willroughly divide into three age categories: Eggs/Hatchlings aged 0-1 years, Juveniles aged 1-24 years Adults aged 24-70 years. The annual survival rates in each category are Eggs/Hatchlings 43%, Juvenile= 77%, Adults 85%. Only adults reproduce, and females produce a mean of 196 eggs/year, giving a per capita rate of about 98 eggs/year for the adult population. a) Find a 3 x 3 structured matrix that describes the change in adult and juvenile populations each year b) Show that this matrix is primitive.
9. The local Pacific green sea turtle reaches maturity at age 24 and has a lifespan of about 70 years. So we willroughly divide into three age categories: Eggs/Hatchlings aged 0-1 years, Juveniles aged 1-24 years Adults aged 24-70 years. The annual survival rates in each category are Eggs/Hatchlings 43%, Juvenile= 77%, Adults 85%. Only adults reproduce, and females produce a mean of 196 eggs/year, giving a per capita rate of about 98 eggs/year for the adult population. a) Find a 3 x 3 structured matrix that describes the change in adult and juvenile populations each year b) Show that this matrix is primitive.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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show the work of part a and b and explain
Transcribed Image Text:9. The local Pacific green sea turtle reaches maturity at age 24 and has a lifespan of about 70 years. So we
willroughly divide into three age categories: Eggs/Hatchlings aged 0-1 years, Juveniles aged 1-24 years,
Adults aged 24-70 years. The annual survival rates in each category are Eggs/Hatchlings 43%, Juveniles
77%, Adults 85%. Only adults reproduce, and females produce a mean of 196 eggs/year, giving a per-
capita rate of about 98 eggs/year for the adult population.
a) Find a 3 x 3 structured matrix that describes the change in adult and juvenile populations each year.
b) Show that this matrix is primitive.
c) Find the eigenvalues and eigenvectors of your matrix (numerically!).
d) What is the long-term distribution of hatchlings, juveniles, and adults in the total population?
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