Answer
$$T=70e^{-kt}+70$$
Work Step by Step
$dT+k(T-70)dt=0$
$dT=-k(T-70)dt$
$\frac{dT}{T-70}=-kdt$
$\int \frac{dT}{T-70}=-\int kdt$
$\ln{(T-70)}=-kt+C$
$T-70=e^{-kt+C}$
$T=e^Ce^{-kt}+70$
Let $A=e^C$
then
$T=Ae^{-kt}+70$
Now applying our initial condition we get
$140=Ae^0+70=A+70$
so $A=70$.
Thus our particular solution is
$$T=70e^{-kt}+70$$
