The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem dN dt - N(1 - 0.0008N), N(0) = 1. (a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedure over a long period of time. | supermarkets By hand, sketch a solution curve of the given initial-value problem.
The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem dN dt - N(1 - 0.0008N), N(0) = 1. (a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedure over a long period of time. | supermarkets By hand, sketch a solution curve of the given initial-value problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem
dN
= N(1 - 0.0008N), N(0) = 1.
dt
(a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedure over a long period of time.
supermarkets
By hand, sketch a solution curve of the given initial-value problem.
N
N
1200
1200
600
1000
1000
500
800
800
400
600
600-
300
400
400
200
200
200
100
5
10
15
20
5.
10
15
20
5
10
15
20
N
600
500
400
300
200
100
5
10
15
20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ca13b2-e90a-4f8b-aa87-163472e135e3%2Fc5b31ada-ec4d-4c10-81f3-0be25bf61a5c%2Fb6a5mga_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem
dN
= N(1 - 0.0008N), N(0) = 1.
dt
(a) Use the phase portrait concept of Section 2.1 to predict how many supermarkets are expected to adopt the new procedure over a long period of time.
supermarkets
By hand, sketch a solution curve of the given initial-value problem.
N
N
1200
1200
600
1000
1000
500
800
800
400
600
600-
300
400
400
200
200
200
100
5
10
15
20
5.
10
15
20
5
10
15
20
N
600
500
400
300
200
100
5
10
15
20
![(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a).
N(t) =
How many supermarkets are expected to adopt the new technology when t = 10? (Round your answer to the nearest integer.)
supermarkets](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88ca13b2-e90a-4f8b-aa87-163472e135e3%2Fc5b31ada-ec4d-4c10-81f3-0be25bf61a5c%2Fktqh8qi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a).
N(t) =
How many supermarkets are expected to adopt the new technology when t = 10? (Round your answer to the nearest integer.)
supermarkets
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