$3-8.$ a$.$ Plot the appropriate polarization curves for the following half cell reactions and determine the corrosion potential and corrosion rate $($current density$)$ assuming activation control of both the anodic and cathodic processes.

$M=M^{+}+e^{-},e=-0\mathrm{.}7V,i_o={10}^{-8}\frac{A}{c}{m}^2,{}_a=+0\mathrm{.}1V$

$2H^{+}+2e^{-}=H_2,e=+0\mathrm{.}1V,i_o={10}^{-6}\frac{A}{c}{m}^2,{}_s=-0\mathrm{.}1V$

$($b$)$ Same as $($a$),$ but assume the limiting current density for the reduction reaction is ${10}^{-5}\frac{A}{c}{m}^2.$ Again determine the corrosion potential and corrosion rate from your plot.