The power output of a wind turbine depends on many factors. It can be shown using physical principles that the power P generated by a wind turbine is modeled by

P − kAv³

where v is the wind speed, A is the area swept out by the blades, and k is a constant that depends on air density, efficiency of the turbine, and the design of the wind turbine blades.

(a) If only wind speed is doubled, by what factor is the power output increased?

(b) If only the length of the blades is doubled, by what factor is the power output increased?

(c) For a particular wind turbine, the length of the blades is 30 m and k − 0.214 kg/m³. Find the power output (in watts, W− m² · kg/s³ ) when the wind speed is 10 m /s, 15 m /s, and 25 m /s.