Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.12 - Modeling Variation - 1.12 Exercises - Page 129: 54

Answer

$80.16$ and $r=0$

Work Step by Step

I. As per the given problem, we have: $r=kx(P-x)$ Here, $k$ is defined as constant of proportionality when the length gets doubled then we have $r_{10}=k(10)(5000-10) \implies 49900k$ and $r_{1000}=k(1000)(5000-1000) \implies 4000000k$ Plug the given data in the above expression, we get $\dfrac{r_{10000}}{r_{10}}=\dfrac{4000000k}{49900k}=80.16$ II. When all the people are infected.there will be no infection spread . Then, we have $x=P$ This gives: $r=kP(P-P)=0$
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