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: 39


See the explanation below.

Work Step by Step

The exponential growth can be written as: $y=y_0e^{-kt}$ ...(1) This implies that $y=y_0e^{-k(3/k)} \implies y=y_0e^{-3}$ we can see that $y=\dfrac{y_0}{e^{3}} \lt \dfrac{y_0}{20} $ or, $\dfrac{y_0}{e^{3}} \lt (0.05)y_0$ Hence, we conclude that after three mean lifetimes we are left with 5% and so, more than 95% disintegrates.
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