Answer
True.
Work Step by Step
The solution of $y'=-k(y-b)$ is
$$y=b+c e^{-kt}.$$
Since $k\gt 0$, then as $t\to \infty$, then $y\to b$ and hence all solutions will tend to $\infty$ as $t\to \infty$.
So the statement is true.
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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) - Preliminary Questions - Page 359: 3
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