$2\mathrm{.}4$ An equal percentage control valve has a $Cv$ of $50$ at $30\%$ valve travel and a $Cv$ of $112\mathrm{.}5$ at $50\%$ valve travel;

$($a$)$ Calculate the $Cv$ at $40\%$ valve travel

$2$

$($b$)$ Calculate the maximum valve $Cv$

$[2]$

$($c$)$ Calculate the valve rangeability

$2$