Explore BrainMass

Population growth and transitions

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Juveniles Adults
Subpopulation size (aged under 15 years) (aged 15 years and over)
(in millions) 1.89 5.31
Birth rate 0 0.0332
Death rate 0.0086 0.0295

The diagram below shows a network model of the changes in the subpopulation sizes from year to year. Here Jn and An denote the sizes (in millions) of the subpopulations of juveniles and adults, respectively, n years after the year 1880. It has been assumed that, in any year, 1/15 of the juveniles become adults.

(a) Explain why the number labeling the pipe from J to An+1 is 0.0661 and the number labeling the pipe from Jn to Jn+1 is 0.9253.
(h) The network model above can be written as a matrix equation of the form
where M is a 2 x 2 matrix. Write down the matrix M.

© BrainMass Inc. brainmass.com December 20, 2018, 2:30 am ad1c9bdddf


Solution Preview

Hello and thank you for posting your question to Brainmass!
The solution is attached below in two files. ...

Solution Summary

The solution shows how to convert the network diagram to a matrix-based system.