in-2012-the-population-of-california-was-38041430-and-the-population-living-in-the-united-states-but

Question

In 2012 the population of California was 38,041,430, and the population living in the United States but outside California was 275,872,610. During the year, it is estimated that 748,252 persons moved from California to elsewhere in the United States, while 493,641 persons moved to California from elsewhere in the United States.$^4$
a. Set up the migration matrix for this situation, using five decimal places for the migration rates into and out of California. Let your work show how you produced the migration matrix.
b. [M] Compute the projected populations in the year 2022 for California and elsewhere in the United States, assuming that the migration rates did not change during the 10-year period. (These calculations do not take into account births, deaths, or the substantial migration of persons into California and elsewhere in the United States from other countries.)

Jack Chen · Accepted Answer

So in this program, we are going to set Happy Jin said have a difference. Um, question by off finding out transition metrics. And so in this case, XK means he has to entrance the first entrance. The population in California and then a second transience the the population, you know elsewhere. So I will say the rest pot. And if we define the variable in this way, the transition matrix in has four engines. So the first intron will be the the rate of people stay in California. And this, in turn, will be the people the right off people left. So I was a leave Californian. So this is the first column. And for the second car in the first century will be the people. Um stay outside and the 2nd 1 will be the people. The rate of people moved to California. So? So if we switch the order in XK, we need to switch the order here too. But I first used this order, um, the tradition matrix. And because Teoh, um, their point is your one night ah, seven. And the 0.0 has your 0.9 aids. 03 So in 98 0 33 So should be if they use five off digit we will have on this is 1967 And for the second column, we have, um, your 0.179 and the 0.998 to what? Okay, So this is our churches, your metrics. And we are looking for X 20 6 20 calls to end times x 19 and recursive li equals to end times and times X to the 80. So in the end, we have entered 20 times, eg zero and the miss case x zero is given. Um, so you see, ex zero. Because to on this So we just use a calculator and that you will gives us, um, the result. The second screen I&#x27;m next year will be this. So just use a calculator in the in the end, we have the solution, x 20 x 20. So you should be extend north 20 x 10 equals Teoh. Um, this So this is a population in the California after 10 years. Since we reiterate this a recursive equation 10 times

Ankit Gupta · Answer

the table represents a population off California from the year 2000 to 2010 so we need to find the estimate of this population, how much it increases every year. So to do that will divide these succeeding tone. By the preceding tome on, we&#x27;ll get the ratio as equal toe. Now. If you&#x27;re dividing every succeeding term with the preceding tome, then we&#x27;ll get the ratio as approximately equal to 1.1 Now we need to model the creation for the population, since it&#x27;s a geometric sequence. So we&#x27;ll need to find the population off today in years, using the in its own formula for geometric sequence, which is usually given us even our race to the bottom friend minus one, which in this case will become equal to 33.87 multiplied with 1.1 drinks to the part off and minus one now. Therefore, the population off for the eight year, which means for any equal to it it or the it&#x27;s dumb or the population after the eight year with people to 33.87 multiplied with 1.1 race to the power of fit minus one, which is equal to 33.87 multiplied with 1.1 raised to the power of seven, which is equal to 38.4 million it&#x27;s

Michael Jacobsen · Answer

in this example, we&#x27;re considering that my gration matrix, which is provide here what it tells us is, for example, if you start living from California and if you&#x27;re considering this entry that it tells us that there is a 1.29% chance that you will migrate to one of the other states in the United States of America. So with this particular matrix But we want to determine is how many much of the population of the United States will remain in California after many years. In other words, what we&#x27;re really trying to find here is the steady state vector que And to that end, we must solve first, the equation that m times X equals X. If we re arrange this equation, it can be brought into the form of M minus died. Any matrix times X equals the zero vector. Let&#x27;s take this equation that we&#x27;ve written here and go to an augmented matrix. So when we consider m minus I, all we&#x27;re really doing is subtracting one from thes entries in the main diagonal of that matrix. So the first entry is going to be negative 0.1 to nine, then I&#x27;ll copy next the point 00 to 7. And since we&#x27;re augmenting with a zero, Vector will have a zero here. Next, let&#x27;s copy 0.129 Then for this century, take one or 10.9973 minus one, and we obtain negative 0.27 And then copy is here again. Now, when we look at these rows, we see that Row two is equal to negative one times. Row one. So that allows us to zero out this row right from the get go in a row reduction. And if we divide Row one by negative 10.129 we&#x27;ll obtain altogether about one a negative point to zero 93 and a zero. So our matrix is now in reduced echelon form, and what it tells us from Row One is that X one equals a positive 10.20 93 times x two and X two is a free variable. It&#x27;s all right. X two equals x two, then the solution X toothy original equation. MX equals X is going to be if we pick a one for X two. Well, have a 0.2093 in the first entry and a one coming from the second entry. Now, this is not the steady state vector que, but we confined it by first taking the entries of X 0.20 93 Adding them together, which is altogether a 1.2093 Then que the state state vector is going to be equal to the reciprocal of this quantity here. So take 1/1 0.20 93 and multiply the vector X. This gives altogether the vector 0.1731 and point a 269 And keep in mind also that the first entry of this vector corresponds to the case where we migrate to California. So if we will allow our initial state vector to be the population of the United States distributed from California and other then since our state&#x27;s debt state vector que involves this century here, we&#x27;ll find that 17.31% off the U. S. A population will my great, too or possibly stay in California after many years

Carson Merrill · Answer

So we&#x27;re giving this linear regression and we want to determine the, uh, predict the population in 1990 given the linear regression. So, in order to do so, we take our linear regression and put 1990 for the X value. And what we get is four million 50,000 273.1. But we&#x27;re told that the actual value is 29,839,250. And this is incredibly incredibly different from our estimation that this shows us right there that one of the biggest issues with linear regression is it does not help us predict extremely long term trends.

Heather Zimmers · Answer

Okay, we&#x27;re doing this problem with a graphing calculator and were given a population growth model. So we go into the y equals menu and we type in that model as given. You can see I&#x27;ve already typed it in. And in this problem, I&#x27;m using an X in place of tea. That&#x27;s what the calculator likes to dio. And we&#x27;re going to say that X equals 15 corresponds to the year 2015. And we want to look at the graph from the year 2015 to the year 2030. So I&#x27;m going to go into the window and I&#x27;m going to change my ex values to 15 as my minimum and 30 as my maximum to correspond with those values. And then for why values remember, these represent the population, so it makes sense. It wouldn&#x27;t be. Negatives will just start with zero, and then I don&#x27;t know exactly what the population values they&#x27;re going to be. The population is growing, and in year zero it&#x27;s 34.696 So suppose I make it go up to 60 for 60 million, and we&#x27;ll see if we like that window choice so Let&#x27;s take a look at the graph. Okay, so there we have it. Now we&#x27;re going to take a look at a table and create a table of values for this time period. So I&#x27;m going to go into table set, and I&#x27;m going to start my table at time. 15. That corresponds to the year 2015. I&#x27;m going to let my table go up by ones and automatically generate values. So let&#x27;s look at the table. So here receive the X values that correspond to the years and the Y values that correspond to the populations. And we can go through and we can go all the way up to t equals 30 if we want to, which will take us to the year 2030. We can keep scrolling, okay. And then for part C, we want to figure out when the population will exceed 50 million. So one way to do it is to keep scrolling in the table until we go above 50 million. Oh, Oh, I thought it was going back down there for a minute. But no, just my imagination. There we go. It exceeds 50 million in year 38 So if you add that to 2000 you get the year 2038 or 2038. Another way to do that would be to go back to your graphing menu, your y equals menu type in a 50 that would put a horizontal line at a height of 50. Go back to your window and change the X max. Maybe we could make it something like 50 to go out 50 years. And then we&#x27;ll look at the graph. Here&#x27;s our function again. And then here comes the horizontal line at a height of 50 and we would look for that intersection. Point so into the calculate menu. First graph. Yes. Oops. Into the calculate menu. Choose Intersect number five. My graphs. Air going again. Okay, first curve. Yes. Second curb. Yes. Give it a guess. Yes. And there we have about 37 would give us a year, uh, would give us a population of 50 million. So that would be the year 2037. So it depends on if you want to go slightly about that, Then you would say 2038

Ian Shi · Answer

all right. So for part A, it&#x27;s very simple. Just plug in the cockpit and divide. We could see that if we were to do that, we get that each preceding year. Um, each year in the future is about 1.1 times what it was before of a part B. The general formula for, um, a geometric Siris for the end term would be a end. The end terms. You go to the first term, you know, it&#x27;s times your rate to the N minus one. In this case, we plug in what we know and we eat. When you see that this formula is 33 put it seven, which is the original, given your data times 1.1 and just calculated from part A, the end minus one. Have a part C We&#x27;re trying to find basically a 28 21 that&#x27;s 2020. That&#x27;s 21 years after 1999. And if we do this to be a 33.87 times one points here, one to the toy with power, which gives us approximately 41.33 I&#x27;m. And then this is measured in millions

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[M] Budget® Rent A Car in Wichita, Kansas, has a …

Problem 11 Medium Difficulty

Answer

a. $\left[\begin{array}{cc}{0.98033} & {0.00179} \\ {0.01967} & {0.99821}\end{array}\right]$
b. The population of California is estimated to be 35,729,000 and the population of the rest of the US is estimated to be 278,190,000.

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

Linear Algebra and Its Applications

Grace H.

Anna Marie V.

Caleb E.

Maria G.

Absolute Value - Example 1

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a. $\left[\begin{array}{cc}{0.98033} & {0.00179} \\ {0.01967} & {0.99821}\end{array}\right]$b. The population of California is estimated to be 35,729,000 and the population of the rest of the US is estimated to be 278,190,000.

Linear Algebra and Its Applications

Grace H.

Anna Marie V.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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

Grace H.

Anna Marie V.

Caleb E.

Maria G.

a. $\left[\begin{array}{cc}{0.98033} & {0.00179} \\ {0.01967} & {0.99821}\end{array}\right]$
b. The population of California is estimated to be 35,729,000 and the population of the rest of the US is estimated to be 278,190,000.

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

Linear Algebra and Its Applications