Precalculus (6th Edition) Blitzer

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

Chapter 3 - Review Exercises - Page 514: 88


a)$$200$$ b)$$45411$$ c)$$500000$$

Work Step by Step

a) When the epidemic began, $t=0$, the number of ill people is$$f(0)=\frac{500000}{1+2499e^{(-0.92)(0)}}=200.$$ b) By the end of the sixth week, $t=6$, the number of ill people is$$f(6)=\frac{500000}{1+2499e^{(-0.92)(6)}} \approx 45411.$$ c) The number of ill people at the limiting size of $f(t)$, $t \to \infty$, tends to as follows:$$e^{-0.92t} \to 0 \quad \Rightarrow \quad f(t)=\frac{500000}{1+2499e^{-0.92t}} \to 500000$$
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