Chapter 3.4, Problem 25E

Remainder Round all answers to two decimal places unless otherwise indicated.

Energy Cost of Running Physiologists have studied the steady-state oxygen consumption (measured per unit of mass) in a running animal as a function of its velocity (i.e., its speed). They have determined that the relationship is approximately linear, at least over an appropriate range of velocities. The table below gives the velocity v, in kilometres per hour, and the oxygen consumption E, in milliliters of oxygen per gram per hour, for the rhea, a large flightless South American bird. (For comparison, 10 kilometers per hour is about 6.2 miles per hour.)

Velocity $\mathit{v}$	Oxygen Consumption $\mathit{E}$
2	1.0
5	2.1
10	4.0
12	4.3

a. Find the equation of the regression line for $E$ in terms of $v$.

b. The slope of the linear function giving oxygen consumption in terms of velocity is called the cost of transport for the animal, since it measures the energy required to move a unit mass by 1 unit distance. What is the cost of transport for the rhea?

c. Physiologists have determined the general approximate formula $C=8.5W^{-0.40}$ for the cost of transport C of an animal weighing W grams. If the rhea weighs 22, 000 grams, is its cost of transport from part b higher or lower than what the general formula would predict? Is the rhea a more or a less efficient runner than a typical animal its size?

d. What would your equation from part a lead you to estimate for the oxygen consumption of a rhea at rest?