Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 6 - Differential Equations - 6.3 Exercises: 37

Answer

97.856%

Work Step by Step

Interpreting the rate of decomposition as: $\frac{dy}{dt}= ky$, integrate to find y $\int \frac{1}{y} dy= \int kdt$ $\ln|y| = kt+C$ $y= Ce^{kt} $ Using the half-life time to be 1599 years $0.5= e^{1599k} $ $ -\ln{2} = 1599k$ $k= \frac{-\ln {2}}{1599}$ Plug back into the Decomposition equation $y=Ce^{\frac{-\ln {2}}{1599}t} $ Find the percentage of a present amount after 50 years $\frac{y}{C} = e^{{\frac{-\ln {2}}{1599}*50}}$ $ \frac{y}{C}= .97855$ percent remaining = 97.856%
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.