A plane crosses the Atlantic Ocean $(3000$ miles$)$ with an airspeed of $500$ miles per hour. The cost $C($in dollars$)$ per passenger is given by

$C(x)=100+\frac{x}{8}+\frac{36,000}{x}$

where $x$ is the ground speed $($airspeed $+-$ wind$).$

$($a$)$ What is the cost when the ground speed is $390$ miles per hour; $490$ miles per hour?

$($b$)$ Find the domain of $C.$

$($c$)$ Use a graphing calculator to graph the function $C=C(x).$

$($d$)$ Complete a table with certain values of $x.$

$($e$)$ Use your table to determine to the nearest $50$ miles per hour, the ground speed that minimizes the cost per passenger?