Problem $5.$ For the data below assume the density of solids is $2\mathrm{.}70M\frac{g}{m^3}$ and complete the following:

$($a$)$ Plot the compaction curves $($format appropriately, manually fit curves to data$)$

$($b$)$ Determine the maximum dry density and optimum water content for each test.

$($c$)$ Compute the degree of saturation at the optimum point for test $A.$

$($d$)$ Plot the $100\%($ZAV$)$ curve as well as the $50,70,$ and $90\%$ saturation lines. Remember that the relationship is not a straight line so you will need to plot a sufficient number of points to determine the curvature.

$($e$)$ Plot the line of optimums based on the data from the three tests.

$\backslash$table$[[A$

$(modified),B$

$(standard),\backslash$table$[[$C$],[($low energy$)]]],[{}_d(M\frac{g}{m^3}),$w $(\%),{}_d(M\frac{g}{m^3}),$w $(\%),{}_d(M\frac{g}{m^3}),$w $(\%)],[1\mathrm{.}873,9\mathrm{.}3,1\mathrm{.}691,9\mathrm{.}3,1\mathrm{.}627,10\mathrm{.}9],[1\mathrm{.}910,12\mathrm{.}8,1\mathrm{.}715,11\mathrm{.}3,1\mathrm{.}639,12\mathrm{.}3],[1\mathrm{.}803,15\mathrm{.}5,1\mathrm{.}755,14\mathrm{.}3,1\mathrm{.}740,16\mathrm{.}3],[1\mathrm{.}699,18\mathrm{.}7,1\mathrm{.}747,17\mathrm{.}6,1\mathrm{.}707,20\mathrm{.}1],[1\mathrm{.}641,21\mathrm{.}1,1\mathrm{.}685,20\mathrm{.}8,1\mathrm{.}647,22\mathrm{.}4],[,,1\mathrm{.}619,23\mathrm{.}0,,]]$