$[$Modelling with $1^{st}-$order ODEs$]$ Raindrops evaporate as they fall, at a rate proportional to the $($spherical$)$ drops' surface area $A(t)=4[r(t){]}^2.$ Find the droplet radius as a function of time, assuming the mass evaporation rate $d\frac{m}{d}t=kA,$ where $k<mn>0</mn>$ is a constant. How long will it take for the droplet to evaporate if its initial radius is $r_0=r(0)=0\mathrm{.}01ft$ and its radius after $10$ s is $r(10)=0\mathrm{.}007ft?$ Suppose the velocity $v(t)$ of a falling drop is given by the solution to $m(t)\frac{dv}{dt}+A(t)kv(t)=m(t)g$ where $g$ is the acceleration due to gravity. Solve for $v(t)$ if the droplet falls from rest.