10 years ago, when the relevant cost index was 125, a nuclear centrifuge cost $40,000. The centrifuge had a capacity of separating 1500 gallons of ionized solution per hour. Today, it is desire to build a centrifuge with capacity of 4500 gallons per hour, but the cost index now is 500. Assuming a power-sizing exponent to reflect economies of scale, x, of 0.7, use the proper model to determine the approximate cost of the new reactor.