Solve.

$5)$ The function $\backslash (\backslash$mathrm$\{$A$\}=\backslash$mathrm$\{$A$\}\_\{0\}\backslash$mathrm$\{$e$\}^\{-0\mathrm{.}01386\backslash$mathrm$\{$x$\}\}\backslash )$ models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault.

i$.$ If $\backslash (\backslash$mathbf$\{400\}\backslash )$ pounds of the material are initially put into the vault, how many pounds will be left after $\backslash (\backslash$mathbf$\{120\}\backslash )$ years?

ii$.$ How many years does it take for $400$ pounds of material intially put into the vault to decay to $200$ pounds material? Round to the nearest whole years.