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$[\mathbf{M}]$ Let $M$ and $\mathbf{x}_{0}$ be as in Example 3a. Compute the population vectors $\mathbf{x}_{k}$ for $k=1, \ldots, 20$ Discuss what you find.b. Repeat part (a) with an initial population of $350,000$ in the city and $650,000$ in the suburbs. What do you find?

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Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 10

Linear Models in Business, Science, and Engineering

Introduction to Matrices

Missouri State University

Oregon State University

McMaster University

Lectures

01:32

In mathematics, the absolu…

01:11

03:05

The population of a city i…

02:35

In a certain region, about…

05:15

Population of a City The p…

01:05

The following formulas giv…

02:58

For the following exercise…

08:18

a. Solve the logistic Equa…

06:10

Overtaking City A has a cu…

08:03

09:07

Suppose that $f(x, y)=20,0…

00:48

Population of a City $A$ c…

for this program. We have initials eight. So for part one, we have initial state x zero because to, um, a tour by one collector which represent the population. And we also have a transition metrics which were present the percentage off the people moving around from city to suburban area off Rome, September Saban area to the city. Also after 20 years, the population, because Teoh, the transition matrix times, eggs, sub knighting. And we used this our transition next recursive Lee, we have until 20 times the unusual states we cheese about, um, 400 on a 74 417,000 400 feet of 55 people live in city and the nearly, um, 580,000 people leaving this around the area. So if we compute the population for each year up to 20 years, way will see that the population is city eyes moron tonic decreasing in the population. In the sabam area, we are eyes increasing. And, uh, when okay, you close to seven. So for the seventh years, the population a city, it's the same as the population in the subject area and the foot part tool. If we change the initial state to be a new um number, and they were keeping a transition man tricks to be the same. We'll see let x 20 years about this, and in this case, the population in the city is mount on the increasing, but it's increase really slow.

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