Five years ago, when the relevant cost index was 120, a nuclear centrifuge cost $40,000. The centrifuge had a capacity of separating 1500 gallons of ionized solution per hour. Today, it is desired to build a new centrifuge with capacity of 4500 gallons per hour, but the cost index now is 300. Assuming a power sizing exponent to reflect economies of scale, x, of 0.75, use the power sizing model to determine the approximate cost (expressed in today's dollars) of the new reactor.

The approximate cost (expressed in today's dollars) of the new reactor is $227,950.71.

Explanation:

This can be calculated as follows:

Cost of centrifuge with 4500 capacities 5 years ago / Cost of centrifuge with 1500 capacities 5 years ago = (Capacity of centrifuge with 4500 capacities / Capacity of centrifuge with 1500 capacities)^Power sizing exponent

Cost of centrifuge with 4500 capacity 5 years ago / $40,000 = (4500 / 1500)^0.75

Cost of centrifuge with 4500 capacities 5 years ago / $40,000 = 2.27950705695478

Cost of centrifuge with 4500 capacities 5 years ago = 2.27950705695478 * $40,000 = $91,180.28

Therefore, we have:

Cost of centrifuge with 4500 capacities now = (Cost index now / Cost index 5 years ago) * Cost of centrifuge with 4500 capacities 5 years ago = (300 / 120) * $91,180.28 = $227,950.71

Therefore, the approximate cost (expressed in today's dollars) of the new reactor is $227,950.71.

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