The head length at age x, H(x) (in m), of the blue whale is related to the total length at age x, T(x), (also in m) by the equation This is an example of an allometric equation, which are discussed in more detail in Section 6.4. In Fig.

6.11 we saw some similar data from humans, where organ weight was plotted against body weight.

H = kT0.62

, for some constant k. The data for this are shown in Fig. 16.2.

a. Differentiate the above expression with respect to x and thus find the relation between the rate of change of head length versus the rate of change of total body length.

b. The relative rate of growth of T, say, is defined by T 0 /T, where the prime denotes differentiation with respect to x.
Find an equation that relates the relative rate of growth of T to the relative rate of growth of H.