The power, P , generated by a wind turbine increases as the wind speed, v , increases, but the rate of increase in power grows dramatically as the wind speed becomes larger. Which function that includes the constant k best represents the relationship between the power generated and the wind speed?

The power should increase as wind speed increases, with its rate of increase growing as the speed becomes larger. A cubic relationship, P = ½kv³, has this behavior because its rate of change is proportional to v², so that rate grows rapidly with wind speed. The square-root and linear choices do not accelerate this way, and k/v decreases as v increases.

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