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) - Preliminary Questions - Page 359: 4


See the discussion below.

Work Step by Step

Newton’s Law of Cooling is: $y'=-k(y-T_0)$ and hence its solution (the temperature) is given by $$y(t)=T_0+c e^{-kt}.$$ So the rate of cooling slows, becuase when $t$ (time) increases, then the term $c e^{-kt}$ decreases and hence $y(t)$ decreases.
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