a-herd-of-american-buffalo-bison-can-be-modeled-by-a-stage-matrix-similar-to-that-for-the-spotted-ow

Question

A herd of American buffalo (bison) can be modeled by a stage matrix similar to that for the spotted owls. The females can be divided into calves (up to 1 year old), yearlings (1 to 2 years), and adults. Suppose an average of 42 female calves are born each year per 100 adult females. (Only adults produce offspring. Each year, about 60$\%$ of the calves survive, 75$\%$ of the yearlings survive, and 95$\%$ of the adults survive. For $k \geq 0,$ let $\mathbf{x}_{k}=\left(c_{k}, y_{k}, a_{k}\right),$ where the entries in $\mathbf{x}_{k}$ are the numbers of females in each life stage at year $k .$
a. Construct the stage-matrix $A$ for the buffalo herd, such that $\mathbf{x}_{k+1}=A \mathbf{x}_{k}$ for $k \geq 0$
b. [M] Show that the buffalo herd is growing, determine the expected growth rate after many years, and give the expected numbers of calves and yearlings present per 100 adults.

Ankit Gupta · Accepted Answer

so I just want to buy this m n plus one de endless one. It&#x27;s a job 151 in Yemen Judo 0.51 I mean bless judo point for again. This is minus 0.5 And when lesson 1.5 do you no to be And plus one is minus 0.5 Eman Bliss No comparing this on this 1.5 Do you no person be if you start with animals? Line toe So, Eman, are you intelligent on beat And no more of Daves in big me lettuce Five blocks So the endless one equal toe minus 0.5 and renders is true Italian plus 1.5 in group AIPAC&#x27;s No solving this this is D emplacement subject 100 So this is so This is the number of deer factor one year and number off M n plus one Just give it Judah 0.51 I m in bless 0.40. So this is do 2.51 into 2000 less Jiro 0.4 live next. So if you want to play this digital digital gentle going to so this is one 0 to 0. And plus this is who lives. So find it. My nemesis. Good. Judo 10 So this must that would be line.

Nicholas Barvinok · Answer

we have the following system of difference Equations n sub one comma T Plus one equals 100 and sub three comity plus 150 and sub for comedy and sub two comma T plus one equals 0.5 and Someone Sebti and Sub three sub t plus one equals 0.2 and sub too. Tiu and and sub four T plus one equals 0.75 and sub three thio, and we want to draw the Matrix diagram for this. So we have four objects and so and this stuff too, and sub three and some four and sub one is what contributes to it after a time stuff. So after a time step from T where a t plus one and we get a contribution from and the sub three by a factor of 100 and a contribution from inside before by a factor of 1 50 Let&#x27;s see now what happens to insult to institute gets a 0.5 contribution from an one and sub three gets a point too. Contribution from in two and in some forgets a 0.75 contribution from N three, and that&#x27;s it

Ankit Gupta · Answer

Hello. Shouldn&#x27;t No way would conduct in this question. This is crushed worse and a support. There are currently 300 females, so 300 are three Teligent female northern sported calls 600 out of 3690 are juvenile. 200 then are so adult. So it&#x27;ll and don&#x27;t be 100 are dead abs. So after five years on the business division, given this is given no plus and 4 to 1 so day and plus one invented toe equal to zero point 33 a one into question. Oh, it is given our jato 0.23 even which is job. 133 and a one, Which is good Question 2100. So in 2100 which gives which gives our six 93 And after five years, so multiply with five. So this is equal to 3465 on this is Joe 0.18 in tow. First year, uh, this is don&#x27;t be 100. So this is equal to it&#x27;s a 36 straight and for five years were deployed with 55 major After five years. This is equal 18 40 summer jobs it gives 2100 23 Eder&#x27;s on our provide. The Heiress No more adult. After five years, 2123 into five, just upper five years. This is a number of others and be we can conclude that the number off all&#x27;s linearly decorating and see if, uh, forest management you can pick them, then their population will encourage.

Nicholas Barvinok · Answer

we have the following system of difference Equations jae sub d plus one equals two are so empty. Age 70 plus one equals 0.9 jae sub t plus 0.8 h sub t plus 0.1 are so empty. And finally our sub t plus one equals 0.1 jae sub t plus point to age sub T plus 0.9 are 70. Now we want to control the matrix diagram. So first of all, we have three objects or well, let&#x27;s start with J H and our. So we want to see what contributes toe what per time step. So we know that J t sub t plus one is to arse empty. So it means in one time step when t goes to t plus one j. The object Jake gets a contribution on Lee from our by a factor of two. H gets a contribution from J by a factor of 0.9 contribution from H itself by factor 0.8 and a contribution from our by factor 0.1. Finally, our for time step gets a contribution from J by a factor of 0.1 from H by a factor of 0.2 and from our itself by a factor of 0.9 and that is our matrix diagram

Nicholas Barvinok · Answer

we have three types of objects in the situation. We have juveniles, sub adults and adults. No adults have, on average 0.33 juveniles per year, which is our time step. So part time step adults contribute two juveniles by a factor of 20.33 0.6. Juveniles on average, survive every time step to pick up some adults and 0.71 Some adults survived to be adults and 0.94 adults survive each year. So here&#x27;s our matrix diagram. Our difference equations are juveniles. AT T plus want the T plus one time step are equal 2.33 adults at the previous time. Step Some adults AT T plus one time steps are equal to 0.6 juveniles at the previous time step and adults at the T plus one time step are equal to 0.71 sub adults at the previous time. Step plus 0.94 adults at the previous time step and to make a matrix, which illustrates the passing of one time step. We want a matrix, which sends J yes and a at a particular time step to the next time step and by the properties of matrix multiplication. We need the dot product of the first row with this column vector to be able to j t plus sub d plus one. So that&#x27;s going to be 0.33 The next one will just be 10.600 in the final row will be 0.71 point 94 and weird.

Problem 18 Easy Difficulty

Answer

For each 100 adults, there will be approximately 38 calves and 21 yearlings.

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Lily A.

Anna Marie V.

Kayleah T.

Kristen K.

Vectors Intro

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For each 100 adults, there will be approximately 38 calves and 21 yearlings.

Linear Algebra and Its Applications

Lily A.

Anna Marie V.

Kayleah T.

Kristen K.

Vectors Intro

Vector Basics - Example 1

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Lily A.

Anna Marie V.

Kayleah T.

Kristen K.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications