University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 7 - Section 7.2 - Exponential Change and Separable Differential Equations - Exercises - Page 411: 50

Answer

a) 94.13 % b) $t \approx 588$ years

Work Step by Step

a) The half life for carbon is 5730 years. so, $k=\dfrac{\ln 2}{5730}$ $C=C_0e^{-\dfrac{\ln 2}{5730}t}$ Now, at $t=500$ $ C=C_0e^{-\dfrac{\ln 2}{5730}(500)}$ so, $C \approx 0.9413 C_0$ This means that 94.13 % of carbon-14 is present in the Ice Maiden. b) The half life for carbon is 5730 years. so, $k=\dfrac{\ln 2}{5730}$ $C=C_0e^{-\dfrac{\ln 2}{5730}t}$ Now, at $C=0.9313 C_0$ $0.9313 C_0=C_0e^{-\dfrac{\ln 2}{5730}(t)}$ so, $t \approx 588$ years
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.