Solution Found!
N(t) of supermarkets throughout the country that are using
Chapter 3, Problem 1E(choose chapter or problem)
The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem.
\(\frac{d N}{d t}=N(1-0.0005 N), \quad N(0)=1\)
(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. By hand, sketch a solution curve of the given initial value problem.
(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a). How many companies are expected to adopt the new technology when t = 10?
Text Transcription:
frac{d N}{d t}=N(1-0.0005 N)
quad N(0)=1
Questions & Answers
QUESTION:
The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem.
\(\frac{d N}{d t}=N(1-0.0005 N), \quad N(0)=1\)
(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. By hand, sketch a solution curve of the given initial value problem.
(b) Solve the initial-value problem and then use a graphing utility to verify the solution curve in part (a). How many companies are expected to adopt the new technology when t = 10?
Text Transcription:
frac{d N}{d t}=N(1-0.0005 N)
quad N(0)=1
ANSWER:Step 1 of 10
a) In this problem we need to find by using the phase portrait concept of section 2.1 to predict the number of super markets that are expected to adopt the new procedure over a long period of time. By hand ,sketch a solution curve of the given initial value problem.