A Leslie Matrix is given below: [ 3.4 3 3 3 ][ 0.6 0 0 0 ][ 0 0.3 0 0 ][ 0 0 0.5 0 ]1) What is the % (percentage) of the 1 year olds that survive into the 2 year old age group? 2) What is the average for 2 year old females to have a female offspring? **Understanding Leslie Matrices in Population Dynamics**A Leslie matrix is used to model the changes in a population divided into age groups over discrete time intervals. Below is an example of a Leslie matrix and some questions based on it:**Leslie Matrix:**\[\begin{bmatrix}3.4 & 3 & 3.5 & 3 \\0.6 & 0 & 0 & 0 \\0 & 0.3 & 0 & 0 \\0 & 0 & 0.5 & 0 \\\end{bmatrix}\]### Questions:(a) There are 4 age groups of the population.(b) \(60\%\) of the 1-year-olds survive into the 2-year-old age group.(c) 2-year-old females have on average 3.5 female offspring.The matrix structure:- The first row represents the fecundity rates (average number of offspring) of each age group.- The sub-diagonal (just below the main diagonal) represents the survival rates from one age group to the next.- All other entries are zero because individuals either die or remain in the same age group (no shrinking).**Explain Diagram:**The matrix provided is a typical Leslie matrix divided into four age groups. The elements of the matrix illustrate the interactions between these groups in terms of fecundity and survival rates:- The top row shows the reproduction rate of each age class.- The immediate sub-diagonal shows the probability of individuals progressing to the next age group. For example, the second element in the second row indicates the percentage of individuals surviving from age group 1 to age group 2.- All remaining entries are zero, indicating that individuals do not transition directly between non-consecutive age groups or age backward.By analyzing this matrix, one can determine the population growth and age distribution over time, which is significant in ecological studies, population ecology, and conservation biology.

(a): since the matrix is 4×4, So, there are 4 age groups of population. (b): from the given…

A Leslie Matrix is given below: [ 3.4 3 3 3 ] [ 0.6 0 0 0 ] [ 0 0.3 0 0 ] [ 0 0 0.5 0 ] 1) What is the % (percentage) of the 1 year olds that survive into the 2 year old age group? 2) What is the average for 2 year old females to have a female offspring?

A Leslie Matrix is given below: [ 3.4 3 3 3 ] [ 0.6 0 0 0 ] [ 0 0.3 0 0 ] [ 0 0 0.5 0 ] 1) What is the % (percentage) of the 1 year olds that survive into the 2 year old age group? 2) What is the average for 2 year old females to have a female offspring?

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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