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 = ax*^{b}. 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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