Finite Math and Applied Calculus (6th Edition)

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

Chapter 9 - Section 9.2 - Exponential Functions and Models - Exercises - Page 646: 99

Answer

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Work Step by Step

An exponential growth model has the form $f(t)=Ab^{t}$, and, when b is a value over 1, the function values become extremely high as t increases. If we use such a model for population growth, it can be used only for a limited time, because as population grows, for example, the food production can not follow indefinitely, so the whole population can not survive with reduced food resources per person. The exponential curve eventually "bends" to a value after which resources can not support any significant future growth. In other words, after a certain time $t$, the exponential model will no longer be applicable.
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