College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.5 - Page 505: 19


about $15,679$ years old

Work Step by Step

In the model for decay, substitute A with $\displaystyle \frac{15}{100}A_{o}$ (15$\%$ of $A_{o})$ and solve for t: $\displaystyle \frac{15}{100}A_{o} =A_{0}e^{-0.000121t}\displaystyle \qquad .../\times\frac{1}{A_{o}}$ $\displaystyle \frac{15}{100}=e^{-0.000121t}\qquad .../$ take ln( ) of both sides $\ln 0.15=-0.000121t\qquad .../\div(-0.000121)$ $ t=\displaystyle \frac{\ln 0.15}{-0.000121}\approx$15,678.677561 The paintings are about $15,679$ years old.
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