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: 23

Answer

$3561$ years

Work Step by Step

Use the radioactive decay model $m(t)=m_0\cdot 2^{-t/h}$ with the given conditions $m(t)=0.65m_0,h=5730$, we have $0.65m_0=m_0\cdot 2^{-t/5730}$ which gives $t=-5730\times log_20.65\approx3561$ years
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