The different members or organs of an individual often grow at different rates, and an important part of allometry involves the study of relationships among these growth rates (recall the Think About It essay at the end of Chapter 1). Suppose x(t) is the size (length, volume, or weight) at time t of one organ or member of an individual organism and y(t) is the size of another organ or member of the same individual. Then the law of allometry states that the relative growth rates of x and y are proportional; that is,

First show that the allometry law can be written as

then solve this separable equation for y in terms of x.

Transcribed Image Text:

y' (t) y(t) x' (t) k- x(t) for some constant k > 0