Q$6$: Five years ago, when the relevant cost index was $135,$ a nuclear centrifuge cost $$32,000.$ The centrifuge had a capacity of separating $1250$ gallons of ionized solution per hour. Today, it is desired to build a centrifuge with capacity of $3500$ gallons per hour, but the cost index now is $270.$ Assuming a power$-$sizing exponent to reflect economies of scale, $x,$ of $0\mathrm{.}72,$ use the powersizing model to determine the approximate cost $($expressed in today's dollars$)$ of the new reactor.