Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 388: 98


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Work Step by Step

The general solution of $y'=4(y-12)$ is $$y=12+c e^{2t}.$$ When $y(0)=20$, then $20=12+c$, i.e. $c=20-12=8$. In this case $$y=12+8 e^{4t}.$$ When $y(0)=0$, then $0=12+c$, i.e. $c=-12$. In this case $$y=12-12 e^{4t}.$$ See the graphs below.
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