Answer
$$t=\frac{1}{4}\ln3$$
Work Step by Step
$6e^{-4t}=2$
Dividing both sides by 6:
$e^{-4t}=\frac{2}{6}=\frac{1}{3}$
Taking the natural log of both sides:
$-4t=\ln{\frac{1}{3}}=\ln({3^{-1})}=-\ln3$
Solving for $t$:
$t=\frac{1}{4}\ln3$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 342: 20
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