Chapter 43. The Power Curve

  • As a company produces more of a product, it learns how to make the product more efficiently. Can we model the relationship between units produced and the time needed to produce a unit?

A power curve is calculated with the equation y = axb. In the equation, a and b are constants. Using a trend curve, we can determine the values of a and b that make the power curve best fit a scatter plot diagram. In most situations, a is greater than 0. When this is the case, the slope of the power curve depends on the value of b as follows:

  • For b > 1, y increases as x increases, and the slope of the power curve will be increasing as x increases.

  • For 0 < b < 1, y increases as x increases, and the slope of the power curve decreases as

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