Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 4 - Section 4.6 - Modeling with Exponential Functions - 4.6 Exercises - Page 380: 20

Answer

$130$ seconds

Work Step by Step

Use the exponential decay model $m(t)=m_0\cdot 2^{-t/h}$ and the given conditions: $h=30, m(t)=(1-0.95)m_0$ $0.05m_0=m_0\cdot 2^{-t/30}$ which gives $0.05=2^{-t/30}$ $2^{t/30}=20$ $t=30\times \log_2 20\approx130$ seconds
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