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
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
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
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