Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.5 - Exponential and Logarithmic Models - 5.5 Exercises - Page 405: 5


(a) $P=Ae^{-rt}$ (b) $t=\ln\sqrt[r] {\frac{A}{P}}$

Work Step by Step

(a) $A=Pe^{rt}$ $P=\frac{A}{e^{rt}}=Ae^{-rt}$ (b) $A=Pe^{rt}$ $\ln A=\ln (Pe^{rt})$ $\ln A=\ln P+\ln e^{rt}$ $\ln A-\ln P=rt$ $\ln\frac{A}{P}=rt$ $t=\frac{1}{r}\ln\frac{A}{P}$ $t=\ln\sqrt[r] {\frac{A}{P}}$
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