Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.4 - Exponential Change and Separable Differential Equations - Exercises 7.4 - Page 401: 29


$2.8 \times 10^{14}$

Work Step by Step

Consider the exponential growth equation as follows: $y=y_0e^{kt}$ As we are given that $y=2$ and $t=0.5$; $y_0=1$ When we have $ t = 1 hour$ Then $2=e^{0.5k} \implies \ln 2=(0.5) k$ or, $k=\dfrac{\ln 2}{0.5}=\ln 4$ Next, at the end of the $24$ hrs, we get $y =e^{24 \ln 4} $ Thus, $y=4^{24} =2.8 \times 10^{14}$
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