Question

This is solving differential equations by sepeartion of variables

Answer 1

$\mathrm dy+k(y-70)\,\mathrm dx=0$

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.