Q$5\mathrm{.}5$ In the study of fluid mechanics, density is found to be influenced by pressure as shown in Table $5\mathrm{.}13.$ Find the appropriate non$-$linear regression model to fit the data set. $($Hint$,$ first plot the graph of density against pressure and confirm type of approximating curve applicable$).$ Next, compute the correlation coefficient.

Table $5\mathrm{.}13$: For Exercise Q$5\mathrm{.}5$

$\backslash$table$[[$Pressure $K\frac{N}{m^2}$ abs$,101\mathrm{.}33,79\mathrm{.}5,47\mathrm{.}22,35\mathrm{.}65,19\mathrm{.}40,14\mathrm{.}17,10\mathrm{.}35,5\mathrm{.}53,2\mathrm{.}97,1\mathrm{.}62],[$Density$,k\frac{g}{m^3},1\mathrm{.}225,1\mathrm{.}007,0\mathrm{.}660,0\mathrm{.}526,0\mathrm{.}312,0\mathrm{.}228,0\mathrm{.}166,0\mathrm{.}089,0\mathrm{.}047,0\mathrm{.}025]]$