Problem $2\mathrm{.}0(25$ Points$)$

Five years ago, when the relevant cost index was $130,$ a nuclear centrifuge cost $$50,000.$ The centrifuge had a capacity of separating $1500$ gallons of ionized solution per hour. Today, it is desired to build a centrifuge with capacity of $4500$ gallons per hour, but the cost index now is $260.$ Assuming a power$-$sizing exponent of $0\mathrm{.}75,$ determine the approximate cost $($expressed in today's dollars$)$ of the new reactor.