11. Purchase of a Product The market research department at a manufacturing plant determines that 20% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 30% of the people who do not purchase the product during any month will purchase it the next month. In a population of 1000 people, 100 people purchased the product this month. How many will purchase the product (a) next month and (b) in 2 months?
11. Purchase of a Product The market research department at a manufacturing plant determines that 20% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 30% of the people who do not purchase the product during any month will purchase it the next month. In a population of 1000 people, 100 people purchased the product this month. How many will purchase the product (a) next month and (b) in 2 months?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Done elementary_linear_algebra_8th_...
2.5 Exercises See CalcChat.com for worked-out solutions to odd-numbered exercises.
Stochastic Matrices In Exercises 1-6, determine
11. Purchase of a Product The market research
whether the matrix is stochastic.
department at a manufacturing plant determines that
20% of the people who purchase the plant's product
during any month will not purchase it the next month.
On the other hand, 30% of the people who do not
purchase the product during any month will purchase
it the next month. In a population of 1000 people,
100 people purchased the product this month. How
many will purchase the product (a) next month and (b) in
2 months?
[1+ 2 1-.
2.
[0.3 0.16 0.25
3. 0.3 0.6
0.3 0.16 0.5
[0.3 0.5 0.2
4. 0.1
0.8 0.1 0.1
0.25
0.2 0.7
[1
12. Spread of a Virus A medical researcher is studying
the spread of a virus in a population of 1000 laboratory
mice. During any week, there is an 80% probability
that an infected mouse will overcome the virus, and
during the same week there is a 10% probability that a
noninfected mouse will become infected. Three
5.
0 1
0 0
1
15
hundred mice are currently infected with the virus. How
many will be infected (a) next week and (b) in 3 weeks?
6.
13. Television Watching A college dormitory houses
200 students. Those who watch an hour or more of
7. Airplane Allocation An airline has 30 airplanes in
Los Angeles, 12 airplanes in St. Louis, and 8 airplanes
in Dallas. During an eight-hour period, 20% of the
planes in Los Angeles fly to St. Louis and 10% fly to
television on any day always watch for less than an hour
the next day. One-fourth of those who watch television
for less than an hour one day will watch an hour or more
the next day. Half of the students watched television for
an hour or more today. How many will watch television
for an hour or more (a) tomorrow, (b) in 2 days, and (c)
in 30 days?
Dallas. Of the planes in St. Louis, 25% fly to Los Angeles
and 50% fly to Dallas. Of the planes in Dallas, 12.5%
fly to Los Angeles and 50% fly to St. Louis. How many
planes are in each city after 8 hours?
8. Chemistry In a chemistry experiment, a test tube
contains 10,000 molecules of a compound. Initially. 20%
of the molecules are in a gas state, 60% are in a liquid
state, and 20% are in a solid state. After introducing
a catalyst, 40% of the gas molecules change to liquid,
30% of the liquid molecules change to solid, and 50%
of the solid molecules change to liquid. How many
molecules are in each state after introducing the catalyst?
14. Sports Activities Students in a gym class have a
choice of swimming or playing basketball each day.
Thirty percent of the students who swim one day will
swim the next day. Sixty percent of the students who
play basketball one day will play basketball the next
day. Today, 100 students swam and 150 students played
basketball. How many students will swim (a) tomorrow,
(b) in two days, and (c) in four days?
15. Smokers and Nonsmokers In a population of
10,000, there are 5000 nonsmokers, 2500 smokers of
Finding State Matrices In Exercises 9 and 10, use
the matrix of transition probabilities P and initial state
matrix X, to find the state matrices X,, X, and X.
one pack or less per day, and 2500 smokers of more
than one pack per day. During any month, there is a
5% probability that a nonsmoker will begin smoking
a pack or less per day, and a 2% probability that a
nonsmoker will begin smoking more than a pack
per day. For smokers who smoke a pack or less per
day, there is a 10% probability of quitting and a 10%
probability of increasing to more than a pack per day.
For smokers who smoke more than a pack per day, there
is a 5% probability of quitting and a 1o% probability of
dropping to a pack or less per day. How many people
will be in each group (a) in 1 month, (b) in 2 months,
and (c) in 1 year?
[0.6 0.1 0.1]
9. P = 0.2 0.7 0.1
0.2 0.2 0,8
[0.1]
X, -0.1
0.8
[0.6 0.2
10. P = 0.2 0.7 0.1
0.2 0.1 0.9
X,-
Cap 2 C Lening A Righa Rned May ecpd wad d de pan Dlei righ d pany aeped d
Ed view ha demedy ed ctd mlly aee lling engho aal igh gui
prien. Conpae laming a
Chapter 2 Matrices
nsumer Preference In a population of 100,000
asumers, there are 20,000 users of Brand A, 30,000
rs of Brand B, and 50,000 who use neither brand.
31. (a) Find the steady state matrix X using the matrix of
transition probabilities P in Exercise 9.
(b) Find the steady state matrix X using the matrix of
transition probabilities P in Exercise 10.
ring any month, a Brand A user has a 20% probability
switching to Brand B and a 5% probability of not
ng either brand. A Brand B user has a 15% probability
switching to Brand A and a 10% probability of not
ne either brand. A nonuser has a 10% probability of
32. Find the steady state matrix for each stochastic matrix
in Exercises 1-6.
33. Fundraising A nonprofit organization collects](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2Fd5d2322a-28e9-420a-9c41-629738fbef11%2Fkxi69zl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2:48
Done elementary_linear_algebra_8th_...
2.5 Exercises See CalcChat.com for worked-out solutions to odd-numbered exercises.
Stochastic Matrices In Exercises 1-6, determine
11. Purchase of a Product The market research
whether the matrix is stochastic.
department at a manufacturing plant determines that
20% of the people who purchase the plant's product
during any month will not purchase it the next month.
On the other hand, 30% of the people who do not
purchase the product during any month will purchase
it the next month. In a population of 1000 people,
100 people purchased the product this month. How
many will purchase the product (a) next month and (b) in
2 months?
[1+ 2 1-.
2.
[0.3 0.16 0.25
3. 0.3 0.6
0.3 0.16 0.5
[0.3 0.5 0.2
4. 0.1
0.8 0.1 0.1
0.25
0.2 0.7
[1
12. Spread of a Virus A medical researcher is studying
the spread of a virus in a population of 1000 laboratory
mice. During any week, there is an 80% probability
that an infected mouse will overcome the virus, and
during the same week there is a 10% probability that a
noninfected mouse will become infected. Three
5.
0 1
0 0
1
15
hundred mice are currently infected with the virus. How
many will be infected (a) next week and (b) in 3 weeks?
6.
13. Television Watching A college dormitory houses
200 students. Those who watch an hour or more of
7. Airplane Allocation An airline has 30 airplanes in
Los Angeles, 12 airplanes in St. Louis, and 8 airplanes
in Dallas. During an eight-hour period, 20% of the
planes in Los Angeles fly to St. Louis and 10% fly to
television on any day always watch for less than an hour
the next day. One-fourth of those who watch television
for less than an hour one day will watch an hour or more
the next day. Half of the students watched television for
an hour or more today. How many will watch television
for an hour or more (a) tomorrow, (b) in 2 days, and (c)
in 30 days?
Dallas. Of the planes in St. Louis, 25% fly to Los Angeles
and 50% fly to Dallas. Of the planes in Dallas, 12.5%
fly to Los Angeles and 50% fly to St. Louis. How many
planes are in each city after 8 hours?
8. Chemistry In a chemistry experiment, a test tube
contains 10,000 molecules of a compound. Initially. 20%
of the molecules are in a gas state, 60% are in a liquid
state, and 20% are in a solid state. After introducing
a catalyst, 40% of the gas molecules change to liquid,
30% of the liquid molecules change to solid, and 50%
of the solid molecules change to liquid. How many
molecules are in each state after introducing the catalyst?
14. Sports Activities Students in a gym class have a
choice of swimming or playing basketball each day.
Thirty percent of the students who swim one day will
swim the next day. Sixty percent of the students who
play basketball one day will play basketball the next
day. Today, 100 students swam and 150 students played
basketball. How many students will swim (a) tomorrow,
(b) in two days, and (c) in four days?
15. Smokers and Nonsmokers In a population of
10,000, there are 5000 nonsmokers, 2500 smokers of
Finding State Matrices In Exercises 9 and 10, use
the matrix of transition probabilities P and initial state
matrix X, to find the state matrices X,, X, and X.
one pack or less per day, and 2500 smokers of more
than one pack per day. During any month, there is a
5% probability that a nonsmoker will begin smoking
a pack or less per day, and a 2% probability that a
nonsmoker will begin smoking more than a pack
per day. For smokers who smoke a pack or less per
day, there is a 10% probability of quitting and a 10%
probability of increasing to more than a pack per day.
For smokers who smoke more than a pack per day, there
is a 5% probability of quitting and a 1o% probability of
dropping to a pack or less per day. How many people
will be in each group (a) in 1 month, (b) in 2 months,
and (c) in 1 year?
[0.6 0.1 0.1]
9. P = 0.2 0.7 0.1
0.2 0.2 0,8
[0.1]
X, -0.1
0.8
[0.6 0.2
10. P = 0.2 0.7 0.1
0.2 0.1 0.9
X,-
Cap 2 C Lening A Righa Rned May ecpd wad d de pan Dlei righ d pany aeped d
Ed view ha demedy ed ctd mlly aee lling engho aal igh gui
prien. Conpae laming a
Chapter 2 Matrices
nsumer Preference In a population of 100,000
asumers, there are 20,000 users of Brand A, 30,000
rs of Brand B, and 50,000 who use neither brand.
31. (a) Find the steady state matrix X using the matrix of
transition probabilities P in Exercise 9.
(b) Find the steady state matrix X using the matrix of
transition probabilities P in Exercise 10.
ring any month, a Brand A user has a 20% probability
switching to Brand B and a 5% probability of not
ng either brand. A Brand B user has a 15% probability
switching to Brand A and a 10% probability of not
ne either brand. A nonuser has a 10% probability of
32. Find the steady state matrix for each stochastic matrix
in Exercises 1-6.
33. Fundraising A nonprofit organization collects
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