8.1.4.26 Geometric and Physical Applications

\ (\ underline {\ mathrm {y} _ {\ text {Sliding:}}} \) Let \ (t (t) \) will be the temperature of the object at time of time \ (t \), and \ (A \) - the constant ambient temperature. Newton's cooling law: \ (t^{\ prime} (t) = k (t (t) -a) \), where \ (k- \) constant. Let \ (t_ {0} \) - the temperature of the object for time \ (t = 0 \). a. Rewrite Newton's law using the substitution \ (u (t) = t (t) -a \ quad \) and use this to find \ (t (t) \), expressed in \ (t_ {0}, a \) and \ (k \). B. You come