Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Test - Page 516: 29


a)$$14$$ b)$$51.3$$ c)$$140$$

Work Step by Step

a) The number of elk initially introduced to the habitat, $t=0$, is$$f(0)=\frac{140}{1+9e^{(-0.165)(0)}}=14.$$ b) The number of elk expected in the habitat after $10$ years, $t=10$, is$$f(10)=\frac{140}{1+9e^{(-0.165)(10)}} \approx 51.3$$ c) The limiting size of the elk population can be found by examining the behavior of $f(t)$ as $t \to \infty$ as follows.$$e^{-0.165t} \to 0 \quad \Rightarrow \quad f(t)=\frac{140}{1+9e^{-0.165t}} \to 140$$
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