Power for flying: The power P required for level flight by an airplane is a function of the speed u of flight. Consideration of drag on the plane yields the model Here a and b are constants that...

Power for flying: The power P required for level flight by an airplane is a function of the speed u of flight. Consideration of drag on the plane yields the model

Here a and b are constants that depend on the characteristics of the airplane. This model may also be applied to the flight of a bird such as the budgerigar (a type of parakeet), where we take a = 7800 and b = 600. Here the flight speed u is measured in kilometers per hour, and the power P is the rate of oxygen consumption in cubic centimeters per gram per hour.68

a. Make a graph of P as a function of u for the budgerigar. Include flight speeds between 25 and 45 kilometers per hour.

b. Calculate P (39) and explain what your answer means in practical terms.

c. At what flight speed is the required power minimized?