Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.3 - Exponential Functions - Exercises 7.3 - Page 390: 2

Answer

$a)$ $-100\ln1000$ $b)$ $\frac{-1}{k}\ln10$ $c)$ $-1$

Work Step by Step

$a)$ $e^{-0.01t}$ = $1000$ $-0.01t$ = $\ln1000$ $t$ = $\frac{1}{-0.01}\ln1000$ $t$ = $-100\ln1000$ $b)$ $e^{kt}$ = $\frac{1}{10}$ $kt$ = $\ln(\frac{1}{10})$ $t$ = $\frac{1}{k}\ln(10^{-1})$ $t$ = $\frac{-1}{k}\ln10$ $c)$ $e^{(\ln2)t}$ = $\frac{1}{2}$ ${(\ln2)t}$ = $\ln\frac{1}{2}$ ${(\ln2)t}$ = $\ln(2^{-1})$ $t$ = $-\frac{\ln2}{\ln2}$ $t$ = $-1$
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