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 – 0.0004N), 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. 2498 X supermarkets By hand, sketch a solution curve of the given initial-value problem. N N N 1200 2500 2500 1000 2000 2000 800 1500 1500 600 1000 1000 400 200 500 500 5 10 15 20 5 10 15 20 5 10 15 20 N 1200 1000 800 600 400 200 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
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 – 0.0004N), 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. 2498 X supermarkets By hand, sketch a solution curve of the given initial-value problem. N N N 1200 2500 2500 1000 2000 2000 800 1500 1500 600 1000 1000 400 200 500 500 5 10 15 20 5 10 15 20 5 10 15 20 N 1200 1000 800 600 400 200 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
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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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
dt
0.0004N),
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.
2498
X supermarkets
By hand, sketch a solution curve of the given initial-value problem.
N
N
2500
2500
1200
1000
2000
2000
800
1500
1500
600
1000
1000
400
500
500
200아
10
15
20
10
15
20
5
10
15
20
1200
1000
800
600
400
200아
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
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