$5\mathrm{.}6$ Sample $4$ from the previous data set was flooded with crude oil, in several steps, in order to displace the brine. The remaining water saturation and $V$ values were measured at each of these displacement steps. Based on the measured data given in the following and other data from problem $5\mathrm{.}5,$ calculate the true formation resistivity $R_t$ as a function of water saturation $S_w$ and subsequently determine the saturation exponent $n$ of the Archie's saturation equation.

$\backslash$table$[[$Water Saturation,$],[($Fraction$),V(V)$

$5\mathrm{.}5$ Six cylindrical core plugs of $2\mathrm{.}54cm$ diameter and $3\mathrm{.}81cm$ length were taken from an Alaskan North Slope reservoir. After cleaning, porosities of all the plugs were measured by a helium porosimeter. Subsequently, all samples were fully saturated with a $0\mathrm{.}07m$ brine such that $S_w=1.$ Each sample was placed in a resistivity apparatus, and $V$ values were measured for a current flow of $0\mathrm{.}01A.$ Determine the formation factor $F,$ for each core plug, and estimate parameters a and $m$ for Archie's formation factor equation.

$\backslash$table$[[$Core Plug,$($Fraction$),V(V)$