Cost of transport: Physiologists have discovered that steady-state oxygen consumption (measured per unit of mass) in a running animal increases linearly with increasing velocity. The slope of this...

Cost of transport: Physiologists have discovered that steady-state oxygen consumption (measured per unit of mass) in a running animal increases linearly with increasing velocity. The slope of this line is called the cost of transport of the animal, since it measures the energy required to move a unit mass 1 unit of distance. Table 5.10 gives the weight W, in grams, and the cost of transport C, in milliliters of oxygen per gram per kilometer, of seven animals.35

a. Judging on the basis of the table, does the cost of transport generally increase or decrease with increasing weight? Are there any exceptions to this trend?

b. Make a plot of ln C against ln W.

c. Find a formula for the regression line of ln C against ln W, and add this line to the plot you found in part b.

d. The cost of transport for a 20,790-gram emperor penguin is about 0.43 milliliter of oxygen per gram per kilometer. Use your plot in part c to compare this with the trend for cost of transport versus weight in the table. Does this confirm the stereotype of penguins as awkward waddlers?

e. Find a formula that models C as a power function of W.