\(\mathrm dy+k(y-70)\,\mathrm dx=0\)
Separating variables gives
\(\dfrac{\mathrm dy}{y-70}=-k\,\mathrm dx\)
Integrating both sides gives
\(\displaystyle\int\frac{\mathrm dy}{y-70}=-k\int\mathrm dx\)
\(\ln|y-70|+C_1=-kx+C_2\)
\(\ln|y-70|=-kx+C\)
Solving for \(y\) gives
\(e^{\ln|y-70|}=e^{-kx+C}\)
\(y-70=e^{-kx}e^C\)
\(y=Ce^{-kx}+70\)
As \(y(1)=140\), you get
\(140=Ce^{-k}+70\)
\(70=Ce^{-k}\)
\(C=70e^k\)
so the particular solution to this ODE is
\(y=70e^ke^{-kx}+70\)
\(y=70e^{k(1-x)}+70\)
Unless you have any more information, you're done.
