Solution
= Solution
Put $\Delta=T_0-T_\infty$. Before either forcing term acts, <Newton's law of cooling> gives
$$
\boxed{T_1(t)=T_\infty+\Delta e^{-at}\quad(0<t\leq1)},
\qquad
\boxed{T_2(t)=T_\infty+\Delta e^{-at}\quad(t>0)}.
$$
= Solution
Put $\Delta=T_0-T_\infty$. Before either forcing term acts, <Newton's law of cooling> gives
$$
\boxed{T_1(t)=T_\infty+\Delta e^{-at}\quad(0<t\leq1)},
\qquad
\boxed{T_2(t)=T_\infty+\Delta e^{-at}\quad(t>0)}.
$$