Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.6 Models Involving y'=k(y-b) - Exercises - Page 359: 1

Answer

See the details below.

Work Step by Step

The general solution of $y'=2(y-10)$ is $$y=10+c e^{2t}.$$ When $y(0)=25$, then $25=10+c$, i.e. $c=25-10=15$. In this case $$y=10+15 e^{2t}.$$ When $y(0)=5$, then $5=10+c$, i.e. $c=5-10=-5$. In this case $$y=10-5 e^{2t}.$$ See the graphs below.
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