According to the six-tenths-factor scaling rule used in preliminary cost estimation, if a similar unit of capacity n times larger is built, its cost is approximately how many times the cost of the original unit?

Introduction / Context:
During early project stages, engineers estimate costs for different capacities using empirical scaling laws. The widely used six-tenths-factor rule states that cost scales sublinearly with capacity because of economies of scale. This question checks your recall of the scaling exponent and how to apply it qualitatively.

Given Data / Assumptions:

• Two similar process units (same technology) differing mainly in capacity.
• Capacity scale factor n = New capacity / Base capacity.
• Cost follows C_new ≈ C_base * n^0.6 for a first-cut estimate.

Concept / Approach:
The six-tenths-factor reflects that doubling capacity less than doubles cost due to shared infrastructure and geometric scaling (surface vs. volume). While 0.6 is a rule of thumb and varies by equipment type, it is a standard starting point when vendor quotes are unavailable.

Step-by-Step Solution:
Let C2 be cost at capacity n times C1.Apply rule: C2 ≈ C1 * n^0.6.Thus, the multiplier relative to C1 is n^0.6.

Verification / Alternative check:
If n = 2, cost multiplier ≈ 2^0.6 ≈ 1.52, showing economies of scale (less than 2x). If n = 10, multiplier ≈ 10^0.6 ≈ 3.98, much less than proportional scaling (10x).

Why Other Options Are Wrong:
n (or duplicate n): Implies linear scaling; ignores economies of scale.n^0.4: Too low for the general rule; some specialized items may have different exponents but 0.6 is the conventional default.

Common Pitfalls:

• Applying the rule outside its validity (different technology or materials).
• Forgetting to adjust for installation factors, inflation, or location indices.

Final Answer:
n0.6