Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Construct a stage-matrix model for an animal species that has two life stages: juvenile (up to 1 year old) and adult. Suppose the female adults give birth each year to an average of 1.6 female juveniles. Each year, 30$\%$ of the juveniles survive to become adults and 80$\%$ of the adults survive. For $k \geq 0$, let $\mathbf{x}_{k}=\left(j_{k}, a_{k}\right),$ where the entries in $\mathbf{x}_{k}$ are the numbers of female juveniles and female adults in year $k .$a. Construct the stage-matrix $A$ such that $\mathbf{x}_{k+1}=A \mathbf{x}_{k}$ for $k \geq 0 .$b. Show that the population is growing, compute the eventual growth rate of the population, and give the eventual ratio of juveniles to adults.c. [M] Suppose that initially there are 15 juveniles and 10 adults in the population. Produce four graphs that show how the population changes over eight years: (a) the number of juveniles, (b) the number of adults, (c) the total population, and (d) the ratio of juveniles to adults (each year). When does the ratio in (d) seem to stabilize? Include a listing of the program or keystrokes used to produce the graphs for (c) and (d).

Suppose that the initial populations are given by $\mathrm{x}_{0}=(15,10)$ The Study Guide describes how to generate the trajectory for as many years as desired and then to plot the values for each population. Let $\mathrm{x}_{\mathrm{k}}=\left(j_{k}, a_{k}\right),$ Then we need to plot the sequences $\left\{j_{k}\right\},\left\{a_{k}\right\},\left\{j_{k}+a_{k}\right\}$ and $\left\{j_{k} / a_{k}\right\}$ Adjacent points in a sequence can be connected with a line segment. When a sequence is plotted, the resulting graph can be captured on the screen and printed (if done on a computer) or copied by hand onto paper (if working with a graphics calculator).

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 6

Discrete Dynamical Systems

Vectors

Campbell University

Oregon State University

Idaho State University

Boston College

Lectures

02:56

In mathematics, a vector (…

06:36

02:05

Construct the matrix diagr…

03:41

In certain parts of the Ro…

02:16

06:57

The amount of medication s…

04:00

To analyze population dyna…

03:52

Rabbit Population Assume t…

10:01

Suppose that a population …

07:09

Fawn Population To model s…

01:25

Catastrophic population co…

13:39

The age/weight relationshi…

for Problem number 17, we have in part a equal to a metrics off 1.6, 4.34 point eight, and part B. We are the determined opening of London 1.6 4.3 4.8 minus London. We'll get love the square minus 4.8 London, minus all 0.48 equal to zero. So the Eigen values off. Eight are given boy longer. Equal to 4.8 was the predictive square root well. 0.8 square minus four boy negative 0.48 over to we get 0.8 negative or positive square root two points 56 over to which will equal to 0.8 positive or negative 1.6 over to equal to 1.2 and negative 0.4 4.4 1.4 The numbers off juveniles and adults are increasing because the largest Eigen values are greater than one. So the eventual growth rate off each age class is 1.2, which is 20% her year 0.5. To find the eventual really little population sizes, we solved a minus 1.2 i boy X equal to zero so negative. 1.2 point 1.6 zero 4.3 Negative 4.4 zero What equal to one negative? Four by 30 You you because you will so x one equals two four by Street X two. We said to be one for metrics for three. Clark See Limited Doesn't seven party Suppose that the initial populations are given by X note equal to 15 and 10? The study guide describes how to generate the trajectory for as many years are desired and then tow plot the values for each population. So that's XK equal toe J k a. Que. Then we need to plot the sequences J k A, Que and J K Plus A, K and J K over a K. So objective points in the secrets can be connected with the line signal segment. When a sequence is plotted, the resulting graph can be captured on the screen, printed. If it was done on a computer, all copied by a hand into paper, a working with graphics calculator. Thank you that the final answer

View More Answers From This Book

Find Another Textbook

In mathematics, a vector (from the Latin word "vehere" meaning &qu…

In mathematics, a vector (from the Latin "mover") is a geometric o…

Construct the matrix diagram for each of the followingmodels.Breedin…

In certain parts of the Rocky Mountains, deer are the main food source for m…

Construct the matrix diagram for each of the followingmodels.Yellow …

The amount of medication still available in the system is given by the funct…

To analyze population dynamics of the northern spotted owl, mathematical eco…

Rabbit Population Assume that a population of rabbits behaves according to t…

Suppose that a population grows according to a logistic model with carrying …

Fawn Population To model spring fawn count $F$ from adult antelope populatio…

Catastrophic population collapse The graph depicting the rate of change of a…

The age/weight relationship of female Arctic foxes caught in Svalbard, Norwa…

04:38

In Exercises $25-28$ , show that the given signal is a solution of the diffe…

17:48

Diagonalize the matrices in Exercises $7-20,$ if possible. The eigenvalues f…

01:31

04:59

Let each matrix in Exercises $1-6$ act on $\mathbb{C}^{2} .$ Find the eigenv…

13:52

Find a QR factorization of the matrix in Exercise 11

07:18

In Exercises 30 and $31,$ find the $\mathcal{B}$ -matrix for the transformat…

02:34

In statistical theory, a common requirement is that a matrix be of full rank…

15:27

Let $\mathbb{P}_{3}$ have the inner product given by evaluation at $-3,-1$ $…

02:09

In Exercises 13 and $14,$ find the best approximation to $z$ by vectors of t…

Let $y_{k}=k^{2}$ and $z_{k}=2 k|k|$ . Are the signals $\left\{y_{k}\right\}…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.