Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 9 - Section 9.4 - Logistic Functions and Models - Exercises - Page 670: 37

Answer

See below.

Work Step by Step

For both an epidemic and a new technology, an amount of time passes, before they "catch on". The epidemic starts off with a low count of infected individuals, and then through social contacts more individuals get infected. A new technology gets applied first by technical aficionados, and then via advertising and "word of mouth" reaches a broader public. Both exhibit an initial exponential growth. After a certain time of spreading/application, the growth tapers off, and the exponential curve is "flattened". In the case of an epidemic, the agent (virus) has less and less individuals it can be transmitted to (limited by population), and in the case of technology, its spread is limited by the market for the technology. Thus, a logistic model is suitable for both.
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