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 669: 26b

Answer

$P(x)\approx 24.70(1.054)^{x}$

Work Step by Step

For small x, $f(x)=\displaystyle \frac{N}{1+Ab^{-x}}\approx(\frac{N}{1+A})b^{x}$ the logistic function grows approximately exponentially with base b. From the given model, $N=86.2,\ A=2.49, b=1.054$ so for small x, $P(x)\displaystyle \approx\frac{86.2}{3.49}(1.054)^{x}\approx 24.70(1.054)^{x}$
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