Answer
$$t=\frac{1}{5}\ln{\frac{100}{7}}$$
Work Step by Step
$7e^{5t}=100$
Dividing both sides by 7:
$e^{5t}=\frac{100}{7}$
Taking the natural log of both sides:
$5t=\ln{\frac{100}{7}}$
Solving for $t$:
$t=\frac{1}{5}\ln{\frac{100}{7}}$
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: 19
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