## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 342: 19

#### 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 $t$: $t=\frac{1}{5}\ln{\frac{100}{7}}$

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