Answer
(a). $T(45)=75+110e^{-0.01277\times45}=136.92$
(b).$t=116.02$ minutes
Work Step by Step
$T(t)=T_s+D_0e^{-kt}$. Whereas, $T(t)$ is a temperature at a time $t$, $T_s$ is the surrounding temperature, $D_0$ is the Initial temperature difference between the object and it's surrounding, $k$ is a positive constant that depends on the type of object.
$T_s=75$, $T(0)=185$, $D_0=185-75=110$,
(a). $T(30)=75+110e^{-k30}=150$,
$110e^{-k30}=75$,
$e^{-k30}=0.68181$,
$-30k=\ln0.68181$,
$k=0.01277$.
Therefore, $T(45)=75+110e^{-0.01277\times45}=136.92$
(b). $T(t)=75+110e^{-0.01277t}=100$,
$110e^{-0.01277t}=25$,
$e^{-0.01277t}=0.2272$,
$-0.01277t=\ln 0.2272$,
$t=116.02$ minutes