$10(15$ points$)$ In a milling operation with no coolant, a cutting speed of $\backslash (400\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$min$\}\backslash )$ is used. The current cutting conditions $($dry$)$ yield Taylor Tool Life equation parameters of $\backslash ($ n$=0\mathrm{.}25\backslash )$ and $\backslash ($ C$=\backslash )1200($ft$/$min$).$ When a coolant is used in the operation, the cutting speed can be increased by

$\backslash (10\backslash \%\backslash )$ and still maintain the same tool life. Assuming $\backslash ($ n $\backslash )$ does not change with the addition of coolant, what is the resulting change in the value of C$?$