$(25$ points$)$ The following data on the density $(k\frac{g}{m^3})$ of papaya puree as a function of temperature have been collected with high precision by a set of experiments at various concentrations $($brix values$).$

a$)$ Predict the density of papaya puree of $20$ brix at $52C$ assuming that a quadratic polynomial represents the data best.

b$)$ Use MATLAB to predict the density of papaya puree of $15$ brix at $63C.$

c$)$ Using your results from part $b,$ predict the temperature of papaya puree having a density of $1038\mathrm{.}7k\frac{g}{m^3}$ at $15.$

$\backslash$table$[[,$Density $\{$:$($kg$/$m$^(3))],[$T$(\backslash$deg C$),10$ Brix,$15\backslash$deg Brix,$20$ Brix,$25\backslash$deg Brix$],[40,1035\mathrm{.}5,1059\mathrm{.}2,1081\mathrm{.}7,1098\mathrm{.}9],[50,1032\mathrm{.}5,1055\mathrm{.}1,1076\mathrm{.}3,1092\mathrm{.}4],[60,1028\mathrm{.}5,1051\mathrm{.}4,1072\mathrm{.}0,1088\mathrm{.}3],[70,1022\mathrm{.}8,1046\mathrm{.}6,1065\mathrm{.}8,1082\mathrm{.}1],[80,1014\mathrm{.}6,1039\mathrm{.}7,1061\mathrm{.}4,1075\mathrm{.}6]]$