A certain species of German beetle, the Vollmar-Wasserman beetle (or VW beetle, for short), lives for at most 3 years. We divide the female VW beetles into three age classes of 1 year each: youths (0-1 year), juveniles (1-2 years), and adults (2–3 years). The youths do not lay eggs; each juvenile produces an average of four female beetles; and each adult produces an average of three females. The survival rate for youths is 50% (that is, the probability of a youth's surviving to become a juvenile is 0.5), and the survival rate for juveniles is 25%. Suppose we begin with a population of 100 female VW beetles: 40 youths, 40 juveniles, and 20 adults. Predict the beetle population for each of the next 5 years.
A certain species of German beetle, the Vollmar-Wasserman beetle (or VW beetle, for short), lives for at most 3 years. We divide the female VW beetles into three age classes of 1 year each: youths (0-1 year), juveniles (1-2 years), and adults (2–3 years). The youths do not lay eggs; each juvenile produces an average of four female beetles; and each adult produces an average of three females. The survival rate for youths is 50% (that is, the probability of a youth's surviving to become a juvenile is 0.5), and the survival rate for juveniles is 25%. Suppose we begin with a population of 100 female VW beetles: 40 youths, 40 juveniles, and 20 adults. Predict the beetle population for each of the next 5 years.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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Transcribed Image Text:A certain species of German beetle, the Vollmar-Wasserman beetle (or VW beetle,
for short), lives for at most 3 years. We divide the female VW beetles into three age
classes of 1 year each: youths (0-1 year), juveniles (1-2 years), and adults (2–3 years).
The youths do not lay eggs; each juvenile produces an average of four female beetles;
and each adult produces an average of three females.
The survival rate for youths is 50% (that is, the probability of a youth's surviving to
become a juvenile is 0.5), and the survival rate for juveniles is 25%. Suppose we begin
with a population of 100 female VW beetles: 40 youths, 40 juveniles, and 20 adults.
Predict the beetle population for each of the next 5 years.
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