8.1.4.26 Geometric and physical applications

\( \underline{\mathrm{y}_{\text {word: }}} \) Let \( T(t) \) be the temperature of the object at time \( t \), and \( A \) be the constant temperature of the environment. Newton's cooling law: \( T^{\prime}(t)=k(T(t)-A) \), where \( k- \) is a constant. Let \( T_{0} \) be the temperature of the object during 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