Question

1. We’re now going to think through one of the most famous scaling problems that scientists have tried to understand. This concerns how animal metabolic rate scales with animal size. Metabolic rate can be considered as how much energy an animal needs to live and survive. We typically measure it in terms of how much oxygen an animal consumes per hour. (You should by now understand the role of oxygen in producing ATP that provides all the energy needs of an animal). Size is just how big an animal is. Let’s first think about what our expectations are with regards energy metabolism and size.
   1. We might expect that energy is primarily used by muscles. In that case, a gram of mouse and a gram of elephant should use exactly the same amount of energy (e.g ATP or O2). If we let oxygen consumption represent energy usage, write the scaling equation that relates oxygen consumption and mass?
2. 2. If we assume that a gram of mouse and a gram of elephant use the same amount of energy, what would you get for the value of b?

Answer 1

a. The relation between the energy usage, oxygen consumption and mass can be explained by the fact that the energy usage is being compared with the oxygen consumption.

Also the more the mass the more will be the oxygen consumption.

So accordingly Oxygen consumption is directly proportional to the mass.

For the equation, Oxygen consumption(O) $\alpha$ Mass(M)

= Oxygen consumption = b(Mass)

where k is a coefficient to equate both the sides.

b. As the mass and oxygen consumption is same for both elephant and mouse,

So the value of b as a coefficient can be found by dividing the oxygen consumption by mass.

b = O/M