$[4$ points$]$ Calculate and plot the excess rainfall intensity hyetograph $[$in$/$h$]$ for the rainfall data given to the right. Use Horton's equation to model infiltration by calculating infiltration rate at the midpoint of each time interval. Use initial and constant infiltration capacities of $1\mathrm{.}60i\frac{n}{h}$ and $0\mathrm{.}55i\frac{n}{h},$ respectively, with a time constant of $0\mathrm{.}40h^{-1}.[$Hint: using Excel to help solve this problem is encouraged $-$ see attached hint for guidance on how to set it up$]$

$\backslash$table$[[$Time $($h$),$Rainfall $($in$)],[0-2,2\mathrm{.}8],[2-4,5\mathrm{.}2],[4-6,3\mathrm{.}3],[6-8,2\mathrm{.}1],[8-10,0\mathrm{.}6]]$

$[3$ points$]$ For the rainfall data in Problem $1\mathrm{.}8,$ calculate the portion of total precipitation that is infiltrated $[\%]$ assuming a constant $-$Index of $0\mathrm{.}55i\frac{n}{h}.$