Answer
(a) $137^\circ F$
(b) $116$minutes
Work Step by Step
(a) Use the Newton's Law of Cooling $T(t)=T_s+D_0e^{-kt}$ with the conditions given $T_s=75, D_0=185-75=110$
since at $, t=30,T(30)=150$, we have $150=75+110e^{-30t}$ which gives $k=-ln(\frac{150-75}{110})/30=0.0128$
and for $t=45$, we get $T(45)=75+110e^{-0.0128\times45}\approx137^\circ F$
(b) Let $T(t)=100$, we get $100=75+110e^{-0.0128t}$ which gives $t=-ln(\frac{100-75}{110})/0.0128\approx116$minutes
